Regardless of what kind of trap (if any) your lavatory has, the floor drain (like any other drain) must also have a trap. Some don’t. You should check that first. Shine a flashlight into it. You should see water, or if you can’t see into it, stick in a length of wire as a “dipstick.” When you pull out the wire it should be wet. The trap may have dried up due to evaporation (a common problem in floordrains). Pour a half gallon of water into it, and that may stop the odor. Also, run water down your fixture drains and listen at the floor drain. If you hear a load gurgling sound, the trap may be siphoning out as water drains into the building drain. That would indicate inadequate venting to the other fixtures on the line.
NtP