Will a fps game lag a little at first since the game is new will it stop lagging when the PC gets used to the game

It shouldn't lag because of a new install. And a PC doesn't need time to get used to the game. If the game lags, ensure your computer meets the recommended requirements for the game. Also close all the open programs you can. Check firewall and anti-virus programs are not the issue by temporarily disabling them. If it still lags contact the technical support or try reinstalling it.