Changing my diet every other day for my workout?

I read that you can’t gain muscle and lose fat at the same time unless you’re overweight or have done heavy lifting before.
On some days, I’ll lift weights and do cardio, and on others I’ll just do cardio (because I can’t lift when my muscles hurt or they won’t repair). When I lift weights, my goal is to gain muscle, so I eat more food with lots of protein. When I do just cardio, my goal is to lose fat, so I eat less and don’t find the extra protein necessary.

Will this diet plan work?
and
Is it a good idea to change my diet pretty much every other day or should I keep it consistent?