What are you attempting to achieve? (Keep it simple and clear)
A tiled floor without using textures.
What is the issue? (Keep it simple and clear - Include screenshots/videos/GIFs if possible)
I’m afraid that the tiles will cause lots of lag.
What solutions have you tried so far? (Have you searched for solutions through the Roblox Wiki yet?)
I played a game called Lag Test 2020 and it creates lag by cloning parts. This is why I believe that the tiles would cause lag.
Tiles:
You should be fine, a few of my games goes up to 10,000 parts and it performs well. Cloning parts in studio is not the same as that what that game does to make you lag.
Lag Test 2020 lags with an insane amount of parts combined with an insane amount of stress on PhysicsService, all done in rapid succession until of course - you lag.
You should start to worry about lag when you finish your build, but keep it mind part count, instances, and textures as you go along and you’ll be fine! Good luck. 
The simple answer to this is: these tiles will not cause lag.
Unless you’re putting a lot of meshes and unions as tiles or whatever thing in abundance, then your game will lag.
A few parts should not cause lag.
If you’re worried about lag, you should get the Part Count plugin. It keeps track of how many parts that are in your game. This should be obvious but, more parts = more lag. Duplicating a few tiles should be absloutely fine and I see no problem, so don’t worry about it. As @Beartikal mentioned, you shouldn’t worry about lag until you’ve completely finished the build.
As I said before, I defo recommend the Part Count plugin to keep track of how laggy your game gets. You should also get multiple testers from different devices to test how they cope with the finished product. 
I don’t like using textures usually, so I just make loads of different parts on flooring like when I want a wood panel floor. I usually just duplicate them, and then union the panels, group them with the base of the floor and I don’t see a lot of lag.