Hyginus

Gaius Julius Hyginus (c. 64 BCE – 17 CE) collated notes on mythology under the heading Fabulae. Number 135 reads:

Laocoon Capyos filius Anchisae frater Apollinis sacerdos contra voluntatem Apollinis cum uxorem duxisset atque liberos procreasset, sorte ductus, ut sacrum faceret Neptuno ad litus. Apollo occasione data a Tenedo per fluctus maris dracones misit duos qui filios eius Antiphantem et Thymbraeum necarent, quibus Laocoon cum auxilium ferre vellet, ipsum quoque nexum necaverunt. Quod Phryges idcirco factum putarunt, quod Laocoon hastam in equum Troianum miserit.

Laocoön, son of Capyos, brother of Anchises, and priest of Apollo, against the will of Apollo had married and had children. He was appointed by lot to sacrifice to Neptune on the shore. Opportunity thus presenting itself, Apollo sent two snakes from Tenedos over the waves of the sea to kill his sons Antiphantes and Thymbraeus. When Laocoön tried to bring aid to them, the snakes killed him, too, in their folds.
The Phrygians thought this happened because Laocoön had thrown his spear against the Trojan Horse. (trans. after Mary Grant)

This brief summary summarises Laocoön's offense against Apollo was marrying and having children. The names he provides for Laocoön's second son, Thymbraeus, signals the connection of Laocoön to Apollo Thymbraeus.