Is the LSD standard for all MY 2005 manuals?

LSD is part of the "sport" package and all 6MT cars have the "sport" package by default. So - yes

I thought so. This past weekend I pulled into traffic and accelerated than my inside tire began to spin. I brought into the dealer and was told that it does not have an LSD. Though he never opened the diff cover, he searched the shop computer and it made no mention of an LSD. Strange. Well NissanNA was contacted and they ordered a new diff - rebuild I guess.

Yes from what I know 04' and up all have it on the 6MT.