Does boosting voltage using MT3608 from 3.7V to 10V module reduces the Lipo battery capacity?
With a 100% efficient power conversion from 3.7 volts to 10 volts, any current taken from the boosted 10 volts will be seen as 10/3.7 (2.702) times as much on the battery so, it's probably better to just consider the battery capacity as unchanged but, in these circumstances it will be dispensing 2.702 times as much current.
Given that the efficiency of a boost converter is probably around 90%, you should account for this also. This would mean that every amp taken at 10 volts will be more likely equivalent to 3 amps at 3.7 volts.

assuming my LED takes 30mA forward current and 3V forward voltage

Three series LEDs will take the same current and this will be equivalent to 90 mA from a 3.7 volt battery. I'm assuming here that the 1 volt difference between 9 volts and 10 volts is used for a circuit for maintaining a constant current into the LEDs.

how long does my LEDs last with that battery if my voltage had been
boosted to 10v

The added complexity here is that as time passes, the battery voltage diminishes and to produce the same 10 volt boosted output requires a larger step-up ratio and, in terms of current drawn from the battery this means more current. So, it's quite a complex relationship if you factor in the diminishing terminal voltage across the battery.