First of all, Minecraft is owned by a Swedish company named Mojang Studios. They do not own the Tlauncher, and it is third-party software that Mojang does not support. However, it is not illegal as well.
Many people assume it is illegal because it is free. Tlauncher is not illegal if you have purchased Minecraft, but if you use it to play free Minecraft, it does become illegal! The point is that the software itself is not illegal, but it can be used for illegal things. This is because you are playing the game for free, which gives money to Tlauncher and not the rightful owner, which falls under Copyright.
The game uses offline servers on which you can play while you are playing an online game. Minecraft with TLauncher is not laggy at all and does not occupy much space, which makes it a favorite among people.