Yes, they will show on the RM-map as well. Waypoints are stored in the internal memory of your unit, and are shown regardless of map.
To transfer the waypoints from your Lowrance to RM, go to "Waypoints, trails...." in "Files" and copy it in USR3 from the internal memory to your memorycard. You can then import that USR3-file into RM. Waypointsymbols are Lowrance-copyright and will not be transferred.
I often use waypoints to mark rocks and obstacles I do not want to run my boat over. I then use those waypoints in RM and GE to create precise polygons for import to RM so the rocks are shown as land in RM even though they are sub-surface. Keeps me from running into them. ;)
Here the arrows point to pilars under a bridge. The polygons used to make this, where drawn in GE based on waypoints placed around the pilars.
On a sidenote, AIS works with RM as well.