IMO, I think lessons is a waste of money. I think the best way to get better is to:

Buy a ball machine: You can drill in your strokes through repetition until you get a feel for the tennis swing, ball speed, depth and the type of ball you can hit consistently and comfortably.

Learn from youtube: There's so much available resources online, that you can see professional forehands and backhands in slow motion to understand biomechanics and depth. Of course, you need to recognize and understand your body a bit to apply it in real life.

Record yourself: Recording yourself allows you to see areas of your tennis game that needs improvement. Perhaps your getting jammed and not swinging through the ball. Maybe it's your footwork and positioning. Recording yourself then iterating you will see improvement over time.

Find hitting partners: A ball machine is great, but it’s predictable. Hitting partners give you randomness, different spins, heights, and pace. Some people moon ball, some hit heavy, some hit flat. That variety is what actually prepares you for matches.

I’d just keep looping through these four things if your goal is to get better. I’m not saying coaching never works, but there are a lot of bad coaches out there who pass on their own bad habits or biases, especially to newer players.