Laena's mount is the she-dragon, Vhagar. Originally ridden by Aegon the Conqueror's elder sister-wife Visenya, Vhagar is the last remaining dragon from the time of Aegon's Conquest.
During the Small Council meeting, there is a mention Lord Grover Tully of Riverrun, an ancestor of Catelyn Tully, and thus Arya, Sansa, and Bran Stark. Grover has a grandson named Elmo and great-grandsons named Oscar and Kermit - all of these are humorously named after characters of Sesame Street (1969).
The pig gifted to Aemond by his brother Aegon, and his half-nephews, Jace and Lucerys, is nicknamed the Pink Dread. This is a reference to Aegon the Conqueror's fearsome dragon, Balerion, who was known as the Black Dread.
Laenor wants to name Rhaenyra's new baby Joffrey. This appears to be in honor of his late friend and lover Joffrey Lonmouth, who was beaten to death by Criston Cole ten years earlier, as shown in the previous episode.
Laena dies by commanding Vhagar to burn her alive; in the book she gave birth to a malformed baby who died, and she died days later. She attempted to fly Vhagar one last time, but died on the step.