Moving a washing machine to another room where a bathroom sink is on the wall behind where the washer is going. Wondering if I can tie into that existing drain and vent with out any issues? Or will I need to run new vent and drain line. The existing lines are 1.5 inch galv. Pipe. Thanks in advance for any help.

If you have a newer washer that 1 1/2" trap and standpipe may bot be large enough to handle the newer more powerful pumps. Can you increase to 2"?
You may cut in a sanitary tee as close to the floor as possible and make the stand pipe at least 36" high. The washer will be wet vented by the lavatory vent. the inspector may not like this set up but it should work without any problems. Besides you're not pulling a permit anyhow are you? Regards, Tom