Yes that is the actual site.
LuckyPatcher has been around forever,
and has a good reputation + community.
Never seen anyone mention anything that it might contain malicious code.
The developer receives revenue through donations and showing ads on the site.
Sadly the project is not open source though.
My guess would be to prevent the hacks / patches it uses,
from being patched / made un-usable.
To be 100% sure though,
you'd have to de-compile the app,
and reverse engineer the source code,
which is a very tedious and time consuming task.