Hello,
pawel16150 wrote: Insert two IN4007 diodes in series in the forward direction
probably only one diode is enough.
My guess is that the "3.7V battery" is simply a lithium-ion cell that is marked that way, that is 3.7V is the "standard" voltage of such a cell. A fully charged lithium-ion cell obtains a voltage of 4.2 V, this voltage must rather withstand this lamp, unless it is written in the instructions "under no circumstances should the battery be charged to 100%". Thus, 5 V - 4.2 V = 0.8 V, i.e. more or less one "normal" diode or two Schottky diodes connected in series.
Voltage breaking with a diode has a disadvantage, however, some power is released on the diode, which is lost, i.e. converted into heat. If you want the smallest possible power loss, look for an impulse lowering converter, with an output voltage of 4 V, which can be supplied with voltage from 5 V, having the highest possible efficiency at the current consumed by your lamp.
best regards