I'm sorry Paul for my delayed reply. I want to know if the lamp is broken both cases (switched on and off). Thank you for your attention
Wow! 20 months later!
Well, this
is a trifle tricky.

When the lamp is powered, you want to monitor whether it is drawing current, so you want a current sensor. Let's see -
this one should probably do.
The 5 Amp
ACS712 gives an analog output of 1 V per 5 Amps, so you need to figure how much current your lamp draws to get an idea of how critical the ADC reading will be; you may want to add an op amp or comparator as per the application notes to make detection easier.
To check the lamp when it is
not powered - well, you have to actually power it! Basically, an opto-coupler across the switch which controls the lamp feeds a few mA through the lamp without lighting it, checking if the filament is OK. If there is no mains supply at all, then you simply will
not be able to determine whether the lamp is intact.