If this problem just started occurring out of the blue, the most likely problem is that the breaker is simply failing. Breakers do not last forever; they trip more easily as they begin to fail.
Just replace it and see if that solves your problem. Make sure you turn the power off at the meter (or the main breaker switch), so that your entire circuit breaker box is dead before you replace the breaker. Take the old one to the store with you to match it because there are different sizes. You also will want to make sure that you replace it with a 20-amp breaker, not a 15-amp breaker, assuming your wiring can handle it (at least 12 gauge wire; see below)
If the problem arose because you just installed the microwave or the additional lights, then your post does not include enough information. It might still be a faulty breaker or you might be overpowering the circuit. The fact that it is a convection microwave is almost irrelevant: the wattage/amperage it pulls is the relevant fact. (I assume it is high, but it could still be under 1000 watts.) The other facts are the number of light fixtures and the wattage of the bulbs or other appliances on that circuit. The Ampacity (Wattage divided by volts) of the breaker also might be too small for the load. (It might be a 15 amp breaker, whereas a microwave will typically need a 20-amp breaker).
Finally, the amperage of the wire the circuit is on is relevant, too. A 10 gauge wire can pull more amps than a 12 gauge wire. Overpowering the wire will cause the breaker to trip excessively, as well. Assuming a 120 volt circuit, here are the ampacity ratings for different wire. Note that the safe ratings are lower than the maximum ampacity so as to give slack for surges and spikes.
10 gauge: 30 amps, (3600 Watts max) Safe at 2880 Watts
12 gauge: 20 amps, (2400 Watts max) Safe at 1920 Watts
14 gauge: 15 amps, (1800 Watts max) Safe at 1440 Watts
That said, it is standard practice if not code for new construction in most jurisdictions to run a seperate circuit for microwaves. In my remodel, I avoided wiring a new circuit by sharing the microwave circuit with the garbage disposal because I have a low-amp disposal and I can make a mental note to not use the two at the same time. (They typically do not get used together in normal use, anyway). However, that is not the preferred way, and would not fly in new construction in my area.
You could also try to re-wire the lights onto another circuit.