Gens Lucretia was originally patrician, but later also included plebeian families. It was one of the most ancient gentes, and the name occurs as early as the reign of Numa Pompilius.
The cognomen of the patrician Lucretii was "Triciptinus". The plebeian families are known by the surnames of Gallus, Ofella, Trio and Vespillo. Carus also occurs as the cognomen of the poet Lucretius. A few Lucretii are mentioned without any cognomen. Praenomina commonly used by members of this gens were Lucius, Publius, Titus, and Spurius.
Titus Lucretius Carus
Titus Lucretius Carus was a first century BCE. Epicurean philosopher, and author of the poem "De Rerum Natura" (Of The Nature of Things). A translation by W. E. Leonard is available at Project Gutenberg. The Latin text can be found at IntraText. John H. Lienhard has posted a commentary on Lucretius' atomism.
Main article: Titus Lucretius Carus
Sp. Lucretius Triciptinus
Sp. Lucretius Triciptinus, the father of Lucretia, whose rape by Sex. Tarquinius led to the dethronement of Tarquinius Superbus and the establishment of the republic. Triciptinus was a member of the senate under Tarquinius, and was appointed Praefectus Urbi by the king, when the latter left the city to prosecute the war against Ardea. After the dethronement of the king, and before the appointment of the consuls, Triciptinus, by virtue of his office of Praefectus Urbi, had the government of the city. He presided at the comitia, in which the first consuls were elected, and for this purpose was probably elected interrex by the patricians, as indeed is expressly stated by Dionysius (v. 11), and might be inferred from analogy.
The two first consuls were L. Junius Brutus and L. Tarquinius Collatinus, 509 BCE. ; and after the death of Brutus in battle, in the course of the same year, Triciptinus was elected to supply his place; but worn out by age, he died a few days after entering upon the office. 
T. Lucretius T. p. Triciptinus
T. Lucretius T. p. Triciptinus, consul in 508 BCE. with P. Valerius Publicola, in which year he fought against the Etruscans, who had attacked Rome under Porsena, and he is said by Dionysius to have been wounded in the battle. Dionysius, however, places the invasion of Porsena in the following year, and accordingly represents Triciptinus as one of the generals of the Roman army under the consuls  . Triciptinus was consul a second time in 504 BCE. with P. Valerius Publicola, in which year the consuls carried on the war against the Sabines with success  .
Lucretius (Triciptinus), was possibly consul in 507 BCE. with P. Valerius Publicola, 
give M. Horatius Pulvillus as the colleague of Publicola.
L. Lucretius T. f. T. n. Triciptinus
L. Lucretius T. f. T. n. Triciptinus, (son of the T. Lucretius T. p. Triciptinus who was consul in 508 B.C.E.), was himself consul in 462 BCE. with T. Veturius Geminus Cicurinus. He fell upon the Volscians, when they were returning from an invasion of the Roman territory laden with booty, and nearly annihilated the whole army. He obtained in consequence the honour of a triumph. In the following year he exerted himself warmly to save Kaeso Quintius, who was brought to trial by the tribune Virginius. 
Triciptinus is mentioned by Dionysius (xi. 15) as one of the distinguished senators who spoke in favour of the abolition of the decemvirate in BCE 449.
Hostus Lucretius L. f. T. n. Triciptinus
Hostus Lucretius L. f. T. n. Triciptinus, son of ,L. Lucretius T. f. T. n. Triciptinus (who was consul in 462 BCE) was consul in 429 B.C.E. with L. Sergius Fidenas. (Livy iv. 30.)
P. Lucretius Hosti f. Triciptinus
P. Lucretius Hosti f. Triciptinus, consular tribune in 419 BCE, and a second time in 417 BCE .
L. Lucretius Flavus Triciptinus
L. Lucretius Flavus Triciptinus, consul in 393 BCE with Ser. Sulpicius Camerinus, in which year he conquered the Aequi. He was consular tribune in 391 B.C.E., when he gained a victory over the Volsinienses ; and he held the same office a second time in 388 BCE, a third time in 383 BCE, and a fourth time in 381 BCE . Plutarch (Camill. 32) represents L. Lucretius as the senator who was usually asked first for his opinion, probably because he was one of the few who had held the rank of consul; and the same writer informs us that Lucretius spoke against the removal to Veii.
See http://www.ancientlibrary.com/smith-bio/3507.html for more.
Lucretius Vespillo was aedile 133 BCE. He is said to have thrown the corpse of Tiberius Gracchus into the Tiber and thus to have obtained the surname of Vespillo ("undertaker"). (Anrel. Vict. de Vir. III. 64 ; respecting the Vespillones, see Diet, of Antiq. p. 559, a, 2d ed.)
Q. Lucretius Vespillo
Q. Lucretius Vespillo, an orator and a jurist, was proscribed by Sulla and put to death. (Cicero "Brutus" 48; Appian, B. G. iv. 44.)
Q. Lucretius Vespillo
Q. Lucretius Vespillo, the son of Q. Lucretius Vespillo the jurist, served in the Pompeian fleet in 48 BCE. He was proscribed by the triumvirs in 43 BCE, but more fortunate than his father, was concealed by his wife Turia in his own house at Rome, till his friends obtained his pardon. In 20 BCE he was one of the deputation which the senate sent to Augustus at Athens to request the latter to assume the consulship for the following year. Augustus declined the honour, and appointed Vespillo, who was accordingly consul with C. Sentius Saturninus in 19 BCE
. He is mentioned in the Res Gestae Divi Augusti.
See http://www.ancientlibrary.com/smith-bio/3582.html for more.
Turia is one of three women listed by the historian Valerius Maximus as examples of womanly virtue:
- "When Quintus Lucretius [Vespillo] was proscribed by the triumvirs, his wife Turia hid him in her bedroom above the rafters. A single maidservant knew the secret. At great risk to herself, she kept him safe from imminent death. So rare was her loyalty that, while the other men who had been proscribed found themselves in foreign, hostile places, barely managing to escape the worst tortures of body and soul, Lucretius was safe in that bedroom in the arms of his wife." 
A lengthy funerary inscription exists 
which is traditionally known as the "Laudatio Turiae". The unnamed subject has sometimes been identified with the Turia married to Q. Lucretius Vespillo, the consul of 19 B.C.E.. W. Ward Fowler states, "...there is a very strong probability that her name was Turia, and that he was a certain Q. Lucretius Vespillo..." 
. N.S. Gill, however, says "It is strongly believed that the woman of this inscription was not Turia." 
Dr. Susan Martin discusses the meaning of the inscription, locating it in its historical context and observing that it shows "...the potential for strength in the conventional model of Roman womanhood." 
The cognomen "Trio" is found on coins but is not found in any ancient writer.
Cn. Lucretius Trio
A "moneyer" active around 135-127 BCE. 
There is an image of a coin of Cn. Lucretius Trio at CoinArchives.
L. Lucretius Trio
A "moneyer" active around 74 BCE. 
There is an image of a coin of L. Lucretius Trio at CoinArchives.
Lucretii in Pompeii
Two houses belonging to Lucretii have been identified in Pompeii. The house of M. Lucretius was found in Regio IX 
and that of M. Lucretius Fronto in Regio V 
Marcus Lucretius Fronto's house in Pompeii is notable for the quantity and quality of the art found therein. 
The following graffito was found in Pompeii: "Twenty pairs of gladiators furnished by Decimus Lucretius Satrius Valens perpetual priest of Nero, son of the Emperor, and ten pairs of gladiators furnished by Decimus Lucretius Valens his son, will fight at Pompeii April 8, 9, 10, 11, and 12. There will be a big hunt and awnings. Aemilius Celer wrote this by the light of the moon." 
Marcus Lucretius Diogenes
A "M. Lucretius Diogenes" is known from a papyrus find in Egypt  .
Livy: The Early History of Rome, Books I-V
The Nature of Things (de rerum natura)
A geneology of Lucretii (PDF)
A one-page PDF chart of many (all?) Lucretii. Online at http://www.virginia.edu/history/courses/meyer/gen/repat/Lucretius-s1.pdf Contributed by Agricola
- ↑ Livy I: 57-58
- ↑ Plutarch, Life of Numa, 21
- ↑ Livy i. 58, 59, ii. 8; Dionysius iv. 76, 82, 84, v. 11, 19; Tac. Ann. vi. .11; Cicero de Rep. ii. 31
- ↑ Livy ii. 8, 11; Dionysius v. 20, 22, 23
- ↑ Livy ii. 16; Dionysius v. 40, foll.
- ↑ Livy; ii. ref>, although some sources