It works good but after certain time it turns on alone and the lamp module wont respond to any commands given.
My question is if I can connect the siren to the module or if connecting it will ruin the module.
ANDRESRODGOM
Plug an incandescent light into the Lamp Module, if it instantly turns ON and can not be turned OFF (which is the way I read your comment, "after certain time it turns on alone and the lamp module wont respond to any commands given") then; Yes, the siren has damaged the Lamp Module.
Lamp Modules do not like it if connected to motors, transformers, TVs, appliances in general. Mainly, they only "play nice" with incandescent lights.
However if the Lamp Module works normally when an incandescent light is plugged into it, then as Brian suggested, it may be an electrical noise problem generated by the siren.