Jon consciously attempts to blind himself to any negative associations about time spent with Liz, only to crash back to reality. The intoxicating powers of romance can effect even those characters inhabiting a world as thick with ennui as Garfield, but the small happiness of time spent with a woman he likes is not enough for Jon. He has to build a scaffolding of self-delusion (look at that lost expression), and fight off even the tiniest unpleasantness. That the date activity was kind of poorly chosen is not a big deal, it's not a character flaw in Liz, and Jon's discomfort could've been avoided by better communication; part of this story is about a thin facade of perfection Jon puts up around Liz. Alternate reading: Jon's horror at the lecture was largely because being reminded of the vulnerability of household pets to tapeworms, i.e. the evening spent with Liz clarified the potential for repulsiveness deep inside his best friend.
The other part is about how Jon and Liz had a good time even though Jon was variously bored and disgusted during the medical lecture. Because while a lot of Garfield is about pointing out how empty and unhappy-making our culture is (Jon's 27 year string of failed dates, Garfield's TV-watching habits), a lot of it is about rooting out the small joys we root out of unexpected crevices. Maybe it's self-delusion in panels one and two... maybe Jon got a weird charge out of getting sick looking at pictures of gastrointestinal systems with his girlfriend. And if the Garfield audience laughed, then maybe we all did.
Q: What does Garfield's rejoinder mean? Is he sarcastically pointing out that since Jon is sick to his stomach he obviously wouldn't want to eat? Or is he implying Jon vomited, and may actually be hungry again? Why do I care about this tiny variable, when the overall meaning of the joke is the same?
Either way, it looks like Garfield is trying to sleep while Jon keeps him awake, babbling about his new girlfriend. The only part that catches his attention is about spaghetti. Who has their priorities in order?