Brother, you're all over the place here lol.
You're talking about mis-matching tires and doing occasional track days?
If you're just doing all this for fun then you're fine.
The 175/55/16 AD07 has an OD of 23.5", and good fitment for the Lotus (I prefer 22.8 to 23.1, but 23.5 is ok)
The 235/45/17 500 has an OD of 25.4, which is really about a half inch too tall, but it'll work. I prefer 24.4.
You need to think about the difference in OD between the two. 1.3" difference, with the rear being higher, is the rake that Lotus prefers.
You're going to be at 1.9 with the rear higher. I think you'll be fine.
But certainly I recommend different specs. You're driving a Lotus bro, not a Civic. There is absolutely no reason you can't have 2 sets of cheap wheels, Rota's if you like and 2 sets of good fitting tires that do 2 different things; one for the street and one for the track. Doing it this way will give you the best of both worlds, and storing your tires properly will allow you to use them effectively for years, especially those track tires.