I have taken Lithium for years. Make sure you drink alot of water.
The tremor should go away after awhile, but if not, ask your doctor to prescribe something for the tremor.
There are meds that stop tremors.

The dose you take is not as important as your blood level.
The therapeutic range for lithium is 0.6-1.2. This can only be determined by a blood test.
If your level is too high, you can get lithium toxicity and the tremor can get worse.

Your doctor should be monitoring your level when you start lithium and then every couple of months.
It does work well for suicidal thoughts, if you are in the therapeutic range..