you are dealing with an old mortar and lathe job.
you need to remove the rest of the mess.
Get a sledge, flatbar, and a straight claw hammer, and remove the mortar and lathe.
Careful of the lathe, it will cut you.
I find the best way is to hammer cracks in a square of about two feet, then hammer the straight claw hammer into these cracks and through the lathe, cutting a square into the lathe. Then use a flatbar to lift the squares up and out of the room. A couple trash barrels will do you good. Don't overfill, and kill your back.
Remove all down to subfloor. And sweep clean.
You should install some sort of underlayment, whether its CBU, hardi, densshield, ditra, what have you. Then install tile using modified thinset. Wait 24 hours before walking, and grout. Wait 3 days after grout cures and seal.
good luck with your project
P.S. Remove the existing mortar and lathe before doing anything. Its work, but necessary. If you try and level it off and install tile, you most likely will get cracks and nightmares
Matt
Cupan Custom Tile and Paint
Charlotte, NC
tile contractor