EM ERJ 175 Captain reported a fumes event during approach descent. The Captain requested priority handling to a diversion airport where a safe landing was accomplished.

Narrative

While descending on the STAR; the EICAS warning message 'LAV SMOKE' illuminated. I could hear the forward lavatory smoke alarm activating. We initiated the LAV SMOKE QRH and called the Flight Attendants to assess the forward lavatory. The Flight Attendant reported no observed smoke. I asked her to verify that the trash can was not smoking and check all around the LAV to confirm there were no remnants of a cigarette. No apparent source for smoke was found and no smoke was directly observed. My initial judgment based on this was that the LAV SMOKE alarm was false. I had the Flight Attendants check a second time and cross check each other that there was no smoke in the lavatory. The First Officer and I elected to continue to ZZZ. Shortly after; the Flight Attendant called back and said that she was smelling an unusual smell (which she later described as an 'oily smell') emanating from or around the lavatory. I asked her if the other Flight Attendant on board smelled this also; and she stated she did. The forward lavatory smoke alarm was still active when I received this call. They stated no smoke was visible; but were clearly concerned about the smell. I did smell a faint odor from the flight deck at this point but cannot accurately pinpoint it. Based on this information; given I now had two separate sources indicating a potential problem; I consulted with the First Officer about options and elected to divert to ZZZ1; which we were nearly right over at this time. Preparations for landing then consumed all of our energy and we did not troubleshoot the LAV SMOKE indication further. We executed a normal landing and taxi to the gate. ATC rolled the trucks for us. In hindsight; there were two additional things I would have done. First; the First Officer and I never donned oxygen. The preparation for landing occurred quickly and my priority was to get on the ground to troubleshoot the combo of LAV SMOKE indication and figure out what the Flight Attendants were smelling. When I switched to 'divert' mindset; putting on oxygen would have been a smart move to ensure the pilots would be protected if fumes intensified. Also; I would have more clearly said we were requesting priority handling. Since I did not clearly say this; the First Officer was confused for a moment exactly what he should say to ATC about our decision to divert.