Should I duplicate the existing road and tag it as you suggested?
I think that the lane is a property of the road, an additional tag, not a separate road that needs to be tagged as “highway”.
But I’m new to osm and I don’t know the secrets of rendering
Well you could mark it as cycleway=lane, and just leave the psv thingy to be. Or you could try to invent your own tagging to specify how the different lanes in a street relate.
Ok, I misunderstood you. Well maybe analogue to cycleway=lane you could also add psv=lane. This might be signalled as wrong by some ‘testing applications’ but it might very well be a new standard in the future.
Well, I hope it won’t be. It mixes up with access tagging (psv=yes/private/no…), unlike cycleway=*, and it also loses information about the lanes’ order. There isn’t an established solution for it right now, however.
A proper solution, imo, needs to use separate OSM objects (probably ways, maybe relations) for lanes because it should be possible to add information to a single lane (e.g. surface=*).