I want to find out if I and my doctor decided when I am disable, and I filed
for long term disability claim for my company, can I get fired or laid off?
Legally, no. Your employer may take whatever action they would have taken in spite of your medical status. As a matter of internal policy though, they may choose to allow your medical leave/disability status override any internal decisions, at least for the time being.
If you are laid off or terminated before your are determined to be disabled for purposes of making an LTD claim, it may be too late to do so. Typically, you must be actively at work in order to file a claim for an income protection benefit such as LTD.
A person, who is nice to you, but rude to a waiter, is not a nice person. (This is very important. Pay attention. It never fails.)