Not directly, unless it is concrete slab, I'd put some mortar, then lay cement backerboard, then more mortar, then the tile. No need to take up the linoleum, just put mortar and then put backerboard on top of it. (I would only put tile on concrete directly or backerboard). Other people might have different results but I've done this with no problems. Especially with the mortar and screws, the backerboard isn't going anywhere. Hope this helps.
I don't know specifically aboout "lanolium" but we had tile successfully installed over ceramic tile and over vinyl sheet flooring. In both cases the professional installer roughed up the surface with a power sander before applying the thin set. Both the tile and the vinyl floors were on a slab.
mcdanard is right-I should have clarified. If this is not on a slab (like most 2nd floor brooms), movement in the floor joists and wood underlayment can cause tile to crack because it can't flex. Bottom line, if it is on a slab you have some options (to be safe you can take up the previous flooring and put directly on slab), but if this is not on the ground floor it's a lot more work and you need backerboard.