If the glaze contains lead, then it shouldn’t be used regardless of whether or not you microwave it. Microwaving doesn’t make it more dangerous.
There are a few things that will make a mug unsuitable for microwave use:
If the clay isn’t properly vitrified (not fired to a high enough temperature), then water will soak into the clay and turn to steam in the microwave. This can break the mug. To test for this, turn the mug upside down to expose the unglazed ring at the base. Place a drop of water on the ring and see whether the drop is drawn into the clay or not. If not, then it’s vitrified.
If the decoration has any metallic accents (typically gold) then these can arc in the microwave.
If the glaze contains lots of iron oxide, it can get too hot in the microwave. Test it be putting the empty mug in the microwave alongside a glass of water (the water is to protect the oven). Run it for a minute, then carefully check to see if the mug is hot to the touch. If it is, then don’t use it in the microwave as you risk burning yourself.
If clay has metal added, this will be to create a speckled appearance for visual interest. This is virtually never done with mass produced ceramics; it’s more often seen in artisanal pottery.