/root/bin/go-lfs

I need to add teh above to PATH. If I simply write "export PATH="$PATH:~/bin/go-lfs" will it cause a problem? I'M assuming that this would remove enerything already in PATH and that might cause problems for the duration of my shell. If so, how could I added it without overwritting what's already there? Thanks.

You can do that (minus the extra quote before $) and it will append to, not replace, the existing PATH. However, using the absolute path is a better practice.

export PATH=$PATH:/root/bin/go-lfs

If you want it to presist from session to session add it to your '.bashrc' file.

I need to be able to run the script in a new shell, without using dot space . command. How can I do that?

What error is the shell giving you when you try to run your script?