They said the lightrail was preventing them from removing it and installing the new one. what to do now?

Remove the offending piece, of course, then put it back after the microwave oven is changed.

Correct. To install a microwave oven, a bracket is attached to the wall, the bottom-rear of the oven is hooked on the bracket, and the oven is swung upward where it is then bolted to the cabinet above. The lightrail prevents the old oven from being swung down (for removal) and the new oven from being swung up.

I had a similar/related problem replacing mine last year. The IDIOT cabinet designer surrounded the OTR microwave with custom trim. I knew when I bought the house that it'd eventually be a problem. Various pieces of it had to be removed or destroyed for access to pull the unit down. Drilled holes on top and hand holes had to be cut at front of a major face piece for access to the electric outlet and top mounting screws. Adhesive tile sheets placed over the hand holes, less destruction needed at the next replacement.

Advice for who to hire? Contacted our kitchen company and of course no response 😬

"Advice for who to hire?"

Did you look underneath the cabinets adjacent to the oven to see how the lightrails are attached? Most likely you can just unscrew the lightrails from the bottoms of the adjacent cabinets to get them out of the way. After the oven is replaced, you can reattach them.

Marie:

I've got a buddy in the Toledo, Ohio, area who specializes in appliance installations. I'll bet he gets $150.00 an hour plus expenses, but his work is amazing.

Update— my husband and dad did it themselves— took about two hours and they’re fairly handy

Here it is;
D

How did the remove it / Any tools they recommend?