Self-hosted image optimization

I met with the following problem.
I have an old WordPress personal site, and now transfer it from shared hosting to VPS with OLS as a web server.
After installing of LSCache I registered domain in and launch an image optimisation. But I have about 4.9k image groups on the site and month quote exhausted in a day. The site is non-commercial and I don't plan to pay any money for support.
The question is - could I do anything to perform optimisation by my vps itself? Because of it load is almost zero.

Thanks a lot for replies and suggestions.
I choose to do image optimization myself so that I can use custom scripts & settings.

You can start with ImageMagick to recompress your jpegs, then use imageoptim to losslessly trim the file size as much as possible both for jpegs and pngs, and then create WebP duplicates of each image using ImageMagick (which got WebP support after version 6.9.something, I believe).

This is a very involved process so you might have to investigate each of those steps one-at-a-time and explore the image output yourself to see if it meets your quality requirements. I'll probably make a post about this on my dev blog in the future to show my settings, but it's not a priority for me right now.
I understand the process but I need some initial instuctions... Why LSCache developers don't foresee an such method as for example WebPExpress ones do?
Ok so you're looking more to see if you can implement whatever processes LSCache and are doing on your own VPS? In that case we'll have to wait for someone official to reply :)