My partner joked that we should take a lie-detector test just to see what it's like. It seems like he might have an ulterior motive. I'm wondering if on the surface it's meant to be something silly just to see if we could "beat it" and get away with lies but I think he's fishing. Maybe he doesn't believe my past or the current state of our relationship. What is the line of questioning? If we do it, should we agree on the questions beforehand? My partner is different like that, frequently having off-the-wall ideas so it doesn't surprise me he would come up with something like this. This one just seems weird and he's mentioned it a few times already.
I've heard of some kinky shit in relationships but this one is, well, yeah, off the wall.
If you've done random, bizarre things before then this could just be another one of them. I have to admit, it does sound kinda fun. It's like that Seinfeld episode. In your situation, it seems a little deeper since it's going to analyze your relationship and potentially cause conflict. (Seinfeld was about Melrose Place.)
My first thought is, is there a company that does this for the public? Is it like a novelty that you can go and do like escape rooms or axe throwing? I've never heard of the public having an outlet to just go somewhere to get polygraphed. (Can you buy a machine online and do them at home?)
So, having said that: does your partner have connections somewhere that this could happen? How much thought has he put into it aside from mentioning it a few times? It's one thing to say, "Wouldn't it be fun to...?" and realistically doing something.
The deeper issue is the "subtle" or "joking" suggestions about doing this that make you feel like your relationship will be under the microscope. I agree. And I also agree that if you agree to be tested, you should set out the line of questions beforehand in the privacy of your own home. If at some point he seems to be taking you down an interrogation route rather than light-hearted questioning, sound the alarm right then and there. Put a stop to it. Then, it's his turn to be in the hot seat: why do you want me to answer this stuff? Why am I being grilled like this? Why don't you trust me?
And here's the thing: most relationship therapists will tell you to phrase statements with "I" -- as in, "I feel like..." or "When I hear that, I..." -- but in this case, I say be direct and point the finger at him. Will it cause conflict? Probably. At the same time, you deserve better than the suspicion of a humiliating lie-detector test in your relationship.
If, after you've heard his proposed line of questions and it's not too intrusive or threatening, I say go for it. It sounds fun! If it turns out he's poking for something, drop him. You need someone who trusts you and can have basic conversations about the relationship.