How to improve FPS on Minecraft servers

Your framerate is not affected by your internet connection. The things that do affect the framerate are in-game things that are the same on servers as in singleplayer.

Servers just tend to have more stuff that lowers your framerate. Lobbies often have a lot of terrain to be generated, lots of players and other entities and tons of particles everywhere, which all lower your framerate.

Of course, you can improve the framerate by going to the video settings and lowering render distance, disable particles, etc. Another way of boosting your computer's performance is by installing modifications to the game, the most popular one being OptiFine.