This is the obvious stuff that most people have done, so lets get right in. The first thing to do is go to video settings and uncheck all of the things (Fullscreen too if it runs really bad on your computer, it can help.) and set the resolution to the lowest. This gave me a decent fps, but not enough to truley run fast like sonic, so we need to go to the next step!

If you tried the last one and it did not work, then there is one last option. In your steam library, right click on Sonic Lost World and click "properties". Then click "Set Launch Options" and type in "--F" ( NO QUOTATION MARKS, JUST --F). This should greatly boost fps for you.

It is worth noting that by doing this, it may cause some unintended glitches, including potentially making some stages unbeatable. If you run into this issue, remove --F, complete the stage, and then re-enable it.

Then it could be a number of things. First of all check if your system meets the minimum requirements. To save you the trouble of looking at the game page, here there are:
MINIMUM:
OS: Microsoft Windows 7 / 8 / 10
Processor: Intel Pentium Dual-Core T4200 (2x2.0GHz) or AMD equivalent
Memory: 2 GB RAM
Graphics: NVIDIA GeForce 8800 (512MB) / ATI Radeon HD 2900 (512MB)
DirectX: Version 9.0c
Storage: 8 GB available space
Sound Card: Sound: 9.0c compatible.
Additional Notes: Memory: 2GB RAM (XP)/3GB RAM (Windows 7 / Vista)

If you dont meet these then the game isnt going to run. you could also try upgrading your drivers, which I cant really help you with, or just setting your computer to run for performance, not quality.
All of my steps should help, If you find something else that helps then please comment about it. Thank you for reading the guide!