I was recently let go from my job of six months due to "not keeping up" with my workload. Do I need to keep this job on my resume (I also waitress as-needed, and have technically been employed with the restaurant for over a year, so there would be no gap in my work history)? If so, how do I state my reason for leaving without being turned down for future jobs?

No, it doesn't have to be on your resume or noted on a job application. If there is no mention of it, you don't have to explain it, and the "gap" is taken care of because of your other job.

Do you want to lie on your resume or tell the truth? I hire for my business - I'd rather hear the truth than find out about a lie.

Was the employment from which you were let go full time and your waitress job part time? I'd be concerned that a call to verify the restaurant job would uncover the other job.

I'd tell the truth.

Why did you leave? You were unhappy with the conditions and/or felt the workload was unreasonable. They terminated you before you could quit.