Which Lowry, the hotel or the Lowry theatre/shopping outlet?
The Lowry hotel is dead easy, turn right out of the Renaissance then walk down Blackfriars St to the crossing at the bottom (dodgy looking pub on the corner) then turn left and walk along Chapel St and the entrance is on your left. If you get to the next main junction by Salford Central Train Station then you've gone too far.
The Lowry outlet and theatre is a right out of the Renaissance and keep walking up past M&S and up Market Street. You will see a tram stop at the top of Market St opposite Debenhams but not the right trams so keep walking up and there is a further tram stop a bit further on in Piccadilly Gardens.
You needs the Eccles tram on the side facing the bus terminals. They come every 12 mins and usually in the sequence of Altrincham, Bury Eccles.
You can get tickets from the machines on the stops and they do random checks so make sure you have one on you.
You need to get off at Harbour City in Salford Quays (stops are Moseley St, St Peter's Sq, G-Mex, Cornbrook, Pomona, Exchange Quay, Salford Quays, Anchorage then Harbour City).
You then walk to your right and cross over and across the big red and white bridge and it's pretty much there. You can see it from the tram stop and usually other people to follow.
Coming back, make sure the trams are still running (the link above).
A black cab would probably cost you a tenner, more at night.