My assumption on that was simple... she just died at childbirth... and Tyrion happened to be the child.
Since Jamie was a Kings Guard for a Targaryen.. maybe you're right and his mother was Targaryen... we know the Lannister house became very strong supplanting Castameer House in their Westerlands (Rains of Castameer song). Perhaps that was with the help of Targaryen support.
From this
Wiki entry on Lady Joana Lannister... based on canon...
- Tyrions mother did die in childbirth
- she was a Lannister.. cousin to her husband Tywin "I died on the john with an arrow in my gut" Lannister
- she may have had an affair years earlier with Aerys Targaryen (who would become the Mad King).. but that was before marrying Tywin and the twins Jamie and Cersie are his...
- but the timing of a tournament to homor Aerys is about the right timing for her to have renewed her affair with Aerys and gotten pregnant with Tyrion... who "killed her" in childbirth.