Generally no. Most lodges require that the MM signing the petition be a member of the lodge being petitioned.
Not necessarily, though, GL rules vary from jurisdiction to jurisdiction. My GL requires two MM recommenders,
one of whom must be a member of the lodge being petitioned, but the other can be from
any lodge in the jurisdiction. I've even heard (albeit secondhand) of GLs allowing brethren from out of state to sign petitions.
"Pearl of the West Lodge 146", however, appears to be a lodge under the GL of FL, whose
standard petition form asks for "Signatures of Members of the Lodge to which the petition is directed: _____ _____", which would suggest you
do need both recommenders to be from the same lodge there.