שמות ד:טז פירוש: רש״י, רשב״ם, ספורנו וטור הארוך

ודבר הוא לך means HE WILL SPEAK to the people ON THY ACCOUNT (לְךָ). This passage is proof, regarding every usage of לך and לי and לו and לכם and להם that follow after the verb דבר, that they all have the meaning of על “on account of”.

ודבר הוא לך, he will do the speaking on your behalf.

לאלוהים, so that he will perform miracles at your behest.