It is. Painted bike lanes that are part of the roadway are always mapped using the `cycleway=lane` tag on the road itself. Separated or protected bike lanes that run alongside a road can either be mapped as a separate `highway=cycleway` or as a `cycleway=track` tag on the road itself.

If you aren't sure which to use, consider whether a cyclist could easily switch between the bike infrastructure and the main travel lanes while riding. If so, it should generally be mapped using the `cycleway` tag on the road.

There's a more detailed guide at https://wiki.openstreetmap.org/wiki/Bicycle#Cycle_features