Well, the two year wait usually is when there is no diagnosed fertility issue. In which case you can still hope for a pregnancy.
If someone has, say, blocked tubes, waiting makes little sense as there is no hope for a spontaneous pregnancy. So it really depends on what your fertility issues are.
As for clinics closing that's really impossible to predict. The economic cost has already been so great that I can't imagine another lockdown, I think it's more likely to have stricter social distancing measures. But obviously I don't have a cristal ball.
As for time to get healthy, it depends on how unhealthy you are to begin with, and how much of a difference a couple of months might make. I honestly don't think that 2-3 months dieting will make a huge difference... You'll lose, maybe, what, 10kg ? Assuming you need to lose that much in the first place. You'll certainly feel better if you change your habits and diet, but I don't think it'll make the difference between a BFP and BFN. Unless you are very overweight, in which case it's more likely to make a difference (and you could potentially lose a lot more weight than 10kg).
And obviously it also depends on your age.
If it was me, I would probably not wait. I'd also try to get healthier, but I wouldn't postpone IVF for that reason (unless very overweight).
As for clinics closing, I'd take the risk because I'd find waiting too hard. Worst case scenario, I'd lose money over the meds if a cycle was cancelled. It'd suck, but less than waiting several months.
But obviously it's a personal decision that depends heavily on your own specific circumstances. And how much losing money would hurt you financially, if a cycle was cancelled.