The problem with lying is you may be asked for an employer reference. This can stop your application dead in its tracks. Plus if you are caught in a lie (depending on the company) you could be blacklisted by their HR department.

I would defo try somewhere else if possible. Try for any General Labor job if you have to, make that known to the agencies if needed. Also try places that are likely to be in need of a seasonal infusion, like Home Depot or small business landscapers.

If all else fails, start networking. I took a sociology elective last semester, and my book explained that speaking to people with whom you have a rapport (trust you to an extent) but are not necessarily a close friend are the ones who are most likely to help land a job (acquaintances preferred, as they reach into a whole different network you and your close friends aren't a part of.)

It won't be a guarantee, but it'll at least get you on the "to interview" list instead of being automatically pre-rejected by the online application filters or tossed if you don't have anything in employment history.