Can I lay premium vinyl flooring over a tile floor?

I think the cracks and grout lines will telegraph through the vinyl. Check with a flooring dealer.

I also think the lines would show through unless it was a very thick vinyl. Can you get a sample piece and lay it on top to check?

You can but the grout lines, cracks, and imperfections will transfer to the vinyl over time.

According to the following website, you can! Check out http://homeguides.sfgate.com/install-vinyl-tiles-over-ceramic-tiles-bathroom-39993.html

How to Install Vinyl Tiles Over Ceramic Tiles in the Bathroom

Vinyl tiles can be a ceramic tile look-alike material.

While some floor materials require very specific and strict underlayments, there is really only one rule with vinyl: it requires a flat surface. As long as you are working with an even, flat surface, your vinyl tiles won’t have "lippage" -- one piece being higher than another. As a general rule of thumb you can install vinyl tiles directly over ceramic tile within certain parameters.

Floor Condition

The floor must be in good condition before you can begin installing vinyl tile. Check for loose, cracked or broken areas of ceramic tile. These areas will need to be removed with a hammer and chisel and filled with a concrete-based thinset mortar. After this cures, it will be flush with the surrounding tiles and you can install directly on top of it. If the floor is in good condition you can install straightaway.

Preparation

You should always pull the toilet before you install the vinyl tile in a bathroom, because the toilet needs to rest on top of the finished surface. In addition, you should remove any trim from around the edges of the room, such as baseboards. Make cuts to match the perimeter of the ceramic tile installation and then cover those perimeter cuts with the baseboards. This hides the required expansion joints around the perimeter from being visible to the naked eye. You would see the cuts if you cut the vinyl tile up against the side of the baseboard. This goes for heater vents and electrical outlets, as well. Everything can be reinstalled after the vinyl tiles are installed.

Normal Installation

If the grout joints are flush with the face of the ceramic tile you can install the vinyl tiles directly over the top of the existing tile installation. You can use self-adhering vinyl tiles for ease of use, or you can go with the old-school method of installing tiles in a bed of adhesive. In this case you must use a trowel depth recommended by your tile manufacturer and smear the adhesive on top of the tile installation with the notched trowel. The tiles are then placed into the bed of adhesive and allowed to dry. Most installations are parallel to the longest wall with a chalk line on the floor to guide the first row and subsequent rows after that.

Sunken Grout Joints

If you have a tile floor with sunken grout joints you will need to first fill those joints so that their surface is flush with the face of the tiles themselves. If you do not, this will carry up through the vinyl tiles, as there will be slight depressions where the grout joints are. Over time, the vinyl will sink or be pressed down into the contour of these depressions, telescoping the grout joints from the ceramic tile installation all the way up through the vinyl tiles. All joints between ceramic tiles must be filled with thinset tile mortar. Apply the mortar with a putty knife or flat metal trowel. Once it dries, you can install the vinyl tiles as you would normally.

The website also discusses the following:

Installing Vinyl Tile Over Existing Vinyl Floor

How to Install Groutable Vinyl Tile

How to Install New Ceramic Floor Tile on Top of Old Ceramic Tile

How to Cover Ugly Shower Tile

How to Tile Over Existing Wall Tile

How to Redo Bathroom Floors Without Ripping Up the Tiles

If you don't want the grout lines to show use a skim coat before laying the vinyl

I'd do a skim coat, then floating vinyl plank

Go to a home store. They will direct you in flooring. It's a mix you set up and spread over the original floor.

see above description

I thought I sent a reply already but seems it didn't go thru. Ask for skim coat at the big box stores flooring dept. Its a layer of material you mix up and spread out to keep the lines from showing through. Send a picture when you are done!