Is it ok to leave pulled dandelions to sit on your lawn to decompose?
What a great question! The pulled dandelions would die and decompose, adding minerals and nitrogen to the soil.
However, there is a significant risk that these invasive weeds might continue to grow on your lawn. The pulled dandelions could still be holding mature seeds, and might then go to seed (so the plants would spread!). And when pulling dandelions, it is important to pull up the entire root (which is very long) or the plants will grow again, from the pieces of root left in the ground. There is also a risk that if you simply leave the pulled plants (including the roots) on the lawn, the roots themselves could re-grow – and start a new crop of dandelions.
Similarly, it is not recommended that you compost dandelions, either. Stubborn weeds like these would likely thrive in the compost and more dandelions would appear after you spread the compost in your garden.
See Saskatchewan Environmental Society. Problem pests: Dandelions
On the other hand, it is a good idea to leave grass clippings on the lawn. These clippings will help stop weeds from germinating by depriving the seeds (e.g., dandelion) from light.