does a copy of leblanc everywhere at once stop itsself from being removed?

Yes — a copy that has LeBlanc, Everywhere at Once's rules text stops its own [Temporary] from killing it, as long as it's sitting at a Battlefield.

Her static "Your [Temporary] effects at my battlefield don't trigger" isn't limited to other permanents — it applies to her own source too (same reasoning as FAQ #10040, just with the copy being the LeBlanc itself). So a Reflection copy of her (e.g., from Deceiver) has her passive plus the granted [Temporary], and at the start of your Beginning Phase the kill trigger simply never fires — Rule 816.

Two caveats: the copy must be at a Battlefield — a copy at your Base (e.g., via Mirror Image) isn't "at my battlefield," so it will still die. And this only stops the trigger from firing: if the [Temporary] trigger is already on the Chain when she arrives, her passive won't remove it (FAQ #11578).