There really is no way to completely eradicate cracks made inside a toilet tank lid; replacing the tank lid is the only permanent solution. However, it is possible to repair the toilet tank, with a little muscle and some adhesives, so that it can still be useful. This task is very easy and should not take more than an hour to complete with the proper supplies on hand.
Step 1 - Prepare the Toilet Tank Lid
In an area of the building that will not get disturbed, lay out some dry towels on the floor or counter. Make sure the length and width of the towels will allow the toilet tank lid to rest on them, and not overhang the towels. Place the lid on top of the towels, the bottom side facing upwards. If pieces have completely broken off arrange them in such a way as to form the original shape and style. Dry the pieces off with a towel as you go to ensure that the adhesive will bond to the porcelain correctly.
Step 2 - Apply the Porcelain Adhesive
After the toilet tank lid pieces have been dried and arranged correctly, begin applying the porcelain adhesive onto the inside of the cracks. Do one section at a time and press the pieces together until the adhesive sets. Be extremely careful when doing this to prevent any more cracks or breakage. Once porcelain has cracked or broken it becomes very brittle.
After one section has bonded, continue on to the next section. Repeat these steps over and over until the cracks have been fixed. Allow the toilet tank lid to sit undisturbed until the adhesive has had ample time to set. Usually allowing it to set overnight will work, but never try to move the toilet tank lid until it is ready, otherwise it will fall apart in your hands.
Step 3 - Replace the Toilet Tank Lid
After the porcelain adhesive has had time to bond and set, carefully pick it up and place it back onto the toilet tank. Be very careful not to bump the edges, or to drop it harshly into place, otherwise it will break and you will have a bigger repair issue than what you originally started with. Cracks, even after they have been repaired, can turn into complete breaks very quickly, so take your time and place the toilet tank lid into place as gently as possible.
As stated before, this type of repair will only last a short time. Once a porcelain toilet tank lid has become damaged with cracks or breaks, it is only a matter of time before it has to be replaced. Using adhesive and being careful not to bump the lid will allow for a temporary fix, but with normal usage of the toilet it will soon form cracks and fall apart again.