Is it safe to take medication lithium carbonate a day after crystal meth use.

I wouldn't touch this question, since you are damned if you do and damned if you don't, so ask the doctor who prescribed the Lithium.
I can't find any studies that address this, other than a survey done of only 6 reports, which didn't provide enough information.
Meth can make all the symptoms worse that you take Lithium for, so I hope you never use it again.