Is the max allowed dose of lithium decided based on the taken dose itself or on the levels of lithium in blood?

It depends: Dosing of lithium depends on the form taken and the patient response, and interactions with other medications. Levels are used to determine if they fall within a range whereby lithium is considered therapeutic. They are also used to confirm toxicity in patients demonstrating suspected side effects . Optimally, response to lithium is determined by clinical presentation in conjunction with level.

Both: Lithium levels are used to guide dosage as "within therapeutic limits" but clinical symptoms are always important-eg, if a person is having side effects but has a "good" lithium level, the dose may still need adjusting. Levels are especially important to guide dose changes and make sure there is not too much lithium in the system, which can be toxic especially to thyroid and kidney. Hope this help