I'm doing research on a Inter-generic cross of Lc. Hauserman's Gala x Blc.Hausermann's Jade. I've read descriptions of this cross has with different "descriptive breeder variations" names. They agree on the color, shape, and size of the flower but then the descriptions deviate when it comes to whether or not the blooms of this cross is fragrant or not. I realize that inter-generic you get a mix of traits that influence offspring and hopefully you get the best of both in the seedlings but can they vary so much that some offspring of this same cross have fragrance and others don't ?

Well they should all be fragrant to some degree. They should have either a citrus or floral scent.
However, these are very complex Cattleya hybrids with several generations in their backgrounds.

Most should be fragrant early in the day. Fragrance is sometimes triggered by the increasing warmth of the sun. Without thoroughly researching these parents or hybrids, one thing jumps out to me! An Lc. is not going to have a guarantee of fragrance. It of course depends on lineage. It is the B in Blc. that often is responsible for the fragrance. That used to be Brassavola digbyana now Rhyncholaelia digbyana. But that frilly green species is often the cause of the fragrance.
Plus you have to keep in mind that not every nose can detect the fragrance or "smells it" as the same fragrance. Every nose is not the same. What is pleasant to my nose may not be pleasant to yours! And if we ask the person standing next to us, they might not smell anything!!

@Cluelessmidwestern there is a webinar on aos.org dealing exclusively with fragrance.
It may not answer your specific question but is full of great information.
Some of their webinars are free to general public and some you need to be a member, not sure which category the fragrance webinar is in.
Fragrance is high on my list of qualities my orchid purchases must have.

The most informative books on Orchid scents are those by Roman Kaiser, I found. Years ago I got my hands on The Scent of Orchids, I still use it to look up the chemical compositions on specific Orchids. Very interesting.
https://www.amazon.com/dp/0444898417/
Not cheap, I just realized....I managed to get my hands on a reasonably priced copy years ago, since we worked for the same company.