Hello, Pelin.
"Lay it on" means to praise someone too much (often in an insincere way). For example, "She really laid it on about how good my cooking was. She said I was the best chef in the world."
You could also say the following phrases which mean the same thing:
1. lay it on thick
2. spread it on thick
3. pour it on thick
3. lay it on a bit thick