Should my cover letter mention that I was laid off from my job?

When writing a cover letter, you should most likely avoid the information that deals with you being laid off from a job. Your cover letter is like a summary of your relevant skills and experience as well as an introduction. You do not provide negative information about yourself during this particular section. You should also not include it in your resume. The only reason to convey this information to future employers is if they directly ask you in an application or in an interview. Otherwise, leave this area alone and leave the past in the past where it belongs.