http://it.wikipedia.org/wiki/Monastero_della_Trinit%C3%A0_di_San_Sergio
http://www.figlididio.it/communio/sergio/sergio.html
http://www.nonsolosalento.it/la_storia_di_San_Sergio__160.html
Il monastero is a more common name.
I have found "laura" whithout quotes only in italian version of a russian site.
Natai, "La Laura della Santa Trinita' di Sergio" may be the literal translation, but it doesn't mean anything in italian.
imogilnitskaya's translation is fine