One lesson a week costs $4000 a year.
But, one lesson a week is basically useless.
Even 2 lessons a week is marginally productive, and that's $8000 a year.
I always recommend spending 10-20hr practicing the handful of things I might give someone in a lesson... before coming back to me..
For most folks, that translates to about 1 lesson per month or at least every couple weeks...
The issue is that 9x out of 10, they don't practice, and rely on the tennis lesson to also be their time to get in their repetition.
I took a lesson from a former ATP guy once. I specifically asked for a list of things to work on at the end of the lesson. I asked to hit with one of his juniors (playing out a set) and had him sit on a bench watching me, just jotting down notes. That list was the basis of at least a years worth of training material. Granted it was 150 for the lesson, but since it was the only lesson I took that year, it was far cheaper than $4k.
You can spend 4k/yr on a lesson per week, but at that point you're just paying for a (good) hitting partner... which is probably a faster way to get beyond 4.0 (than taking a lesson per month). But if how fast you get to say a 5.0 level, is important, then you should consider taking lessons daily.
If you're gonna pay for hitting partner anyway, you could save quite a bit money hiring someone just to hit for like $20-30/hr or something (basically to be your ball machine)... or you could just buy an actual ball machine

i prefer my instructor to NOT hit with me, and spend all his time just watching me, anyway.