Maybe! I would remove the linoleum if it was installed after 1975. Just don't make any dust in the process, by spraying it lightly with water.
To set the backerboard, use 1/2" Hardibacker and set it in a bed of latex modified thinset and screw it to the floor every 8" each direction. Try to line up the screws to hit the joists for the best job. Tape all the joints with fiberglass mesh tape. Then use the same thinset mix for the tile.
For a lot more information, read the tile topic on my website at www.bobf.info.