Should I put a job that I was fired from on my resume?
Yes, you should put a job you got fired from on your resume. If one of your past positions is relevant to the job you want, you should always list it on your resume — even if you were let go from that job.
Do I have to say I was terminated?
In this situation you don't have to lose all hope. According to John Crowley, who works in content and marketing at HR-software company People, an employer doesn't need to know whether or not you were fired from your previous job, and there is no legal obligation to disclose this information.
Can you lie about being fired on a job application?
Telling the truth on a job application or in an interview -- even if painful -- can actually endear you to a prospective employer, particularly if you explain the circumstances that led to the termination. Don't volunteer the fact that you were fired unless specifically asked -- but don't lie about it if you are.