I am not a tile installer or expert but I did tile my kitchen floor last year and I did a lot of research.
Are you tiling directly onto the ply which will become your keezer lid? If so, you should look into using a modified thinset. Wood absorbs moisture, but you need moisture for the thinset to cure. Ideally, you wouldn't be tiling over wood, you would be tiling over cement board/hardiboard, cement, ditra, etc., but this is a special application. As for grouting, since you are tiling over wood, look to find something that's flexible, otherwise, as the wood contracts/expands, it'll crack the grout.
If there's no insulation between the keezer and the ply, your ply will be subject to cold temps causing it to shrink which can lead to cracked grout lines.
Also consider that tile is very heavy. 1/2" ply may not support the weight, not to mention, you'll have one heavy lid. But then again, this is a small application so who knows!
Don't sweat tiling (figure of speech really)! I did my kitchen floor, on a diagonal. It was my first time tiling. It was hard, back breaking work but the end result is beautiful.