If i were to change my gamertag would i lose my stats and other information regarding the LE of Halo 4?
Nope, changing your GT shouldn’t affect stats or anything like that. It might just take a couple games for the servers to fully catch on though.
Nope! At least, it shouldn’t. I believe your stats are linked to a UUID that isn’t dependent on your gamertag - so a change in your GT won’t make the system believe your account is new (therefore, with no stats), because it sees the stats attached to your UUID.
As snickerdoodle mentioned, it will likely take a few games or two for the system to catch up to the change, though.