[villagetinker]

MAPEI makes a colored grout sealer that matches original grout color, I am in the process of doing this at a neighbor, messy but looks great. As for the cracked tiles, you may need to determine what caused the cracking in the first place. Tile over concrete needs a crack barrier layer, this allows the concrete to move (crack) without cracking the tile. If this was not done on your lanai, replacing the tile may fix the problem for a short time and then they may crack again. You will know if you have the necessary barrier when the tile is removed.

IMHO, if you do not have the crack barrier, I would plan on having the entire tile floor removed, the concrete surface cleaned, a crack barrier installed, and new tile and grout. You can call MAPEI about possibly using a flexible thin set for the repair, but I am going to guess that you will get cracking at the grout lines.