<<"I want to know how I can go by car from Lucerne to The Hammetschwand Lift.">>
I suspect many of us might like to know that. ;-)
You must walk in on the Felsenweg from Bürgenstock. That will bring you to the bottom of the elevator.
Or. climb without elevator all the way up to Hammetschwand from the road on the south side of Trogenalp, and walk out the platform to the top of the elevator. Then you can go down on the elevator. ;-)
To go all the way to the top on foot, which adds a hundred or two hundred meters to your climb, climb up to the top (Hammetschwand) on a trail up the south side of Trogenalp, for example, from near Honegg or closer to Waldheim. Those trails are accessible from the road between the parking lot near Trogen and Waldheim/ Bürgenstock.
I always have driven up from Buochs and Ennetbürgen, then parked at the parking area at 899 meters at the top near Honegg. From there, I walk in (west) to Bürgenstock, (actually Waldheim, I guess) then make a hairpin right turn at the chapel, and go out and up the Felsenweg.
My knee is giving me trouble, so I am planning to check with Tourist Info in Luzern ( by track #1 at the Hbf) to see if I can drive up from the other direction ( from Stanstad) and park near the hotels which are undergoing reconstruction.
I think the funicular from near Kehrsiten might be closed due to construction. If not, it would get you to Bürgenstock from the lake boat landing below.
This map may clarify the lay of the land:
map.geo.admin.ch/?X=20 5956.61&Y=672704.68&zo om=8&lang=en&topic=swi sstopo&bgLayer=ch.swisstopo.pixelkarte-fa rbe
The elevator is marked "Aufzug." You can see it in the picture with the red arrow. If you look carefully, you can also see where the Felsenweg makes its way to the foot of the elevator.
On the map, the heavy dashed line is the cantonal boundary. The Felsenweg is the lighter dashed line to the north of the boundary..