I've got a couple guinea pigs. one assumes the tarp is the limit of his territory, whether or not there's fencing.
the other one regularly goes wandering, but respects the areas I've said are off limits. and she knows she has to get back to her territory - the tarp - to get any treats.
so it's entirely possible this bunny recognizes his "room", as defined by the new rug.
"Hey, I need to use my lunch break to get away from work things/have some quiet down time. Give me a break and I'll be better for the afternoon." Subjects you don't want to discuss: "Oooh, that doesn't seem like a topic appropriate for work. What about [thing you are comfortable discussing, work thing]."
I highly recommend becoming very willing to spend time discussing one personal thing so they feel like they're making a connection. I use my pets, but you can use a sports team as some others suggest, or a hobby you don't mind sharing, like your progress on painting minis/knitting that sweater/book you're reading/ latest album from favorite musician. Extroverts want a connection, give them a little and redirect to that thing when they probe.
If your boss persists in bothering you at lunch, ask if you should clock in since this is a work discussion, or if it's really your personal time to use as you wish.
If they persist in bringing up wildly inappropriate topics like sex, say that you're uncomfortable. Make it obvious they're being weird at work. saying "I don't like discussing my sexual preferences at work", or similar, loud enough for others in the breakroom to hear should make them uncomfortable. if that doesn't get you anywhere, there are protections in the US for some things. go to HR, explain you've tried explicitly telling them not to talk to you about whatever inappropriate topic, and it's continuing. Call out that you're feeling harassed by them continuing to bring up this subject that is not work related. HR might want to try a mediated discussion about it; 1 is reasonable, multiple is not.
if it gets to where you need HR and are worried about your legal rights, find a local worker's rights lawyer to provide advice. they should be able to tell you what is reasonable effort from the company to fix the situation. be prepared to lose your job if it gets this far.
you shouldn't have to discuss sex at work as small talk. it can come up in some jobs (medicine, sex work) but shouldn't be in most workplaces, and there are protections from this kind of harassment in the US.