Lichens & Liverworts
These make for some strange growths on the soil surface.
These are neither plant nor fungus but a combination of both; see image above.They are very unattractive and generally will only live on problem soils where they can out compete the grass quite easily. As can be seen from the photo this is a very unhealthy bit of lawn covered in moss and lichen.
Treating them with chemicals is difficult as nothing is going to work too well. The most sensible approach is to address the cause of the problem. This will quite often be dry and compacted soils, heavy thatch and poor nutrition and lawn care. Undertaking a renovation programme of aeration and scarifying may work but do understand that when lichens move in it means your lawn is in critical condition!
Some people find these very attractive. Admittedly the green colour is often quite fantastic. They are related to mosses and favour the dampest and shadiest areas of your lawn. In fact when the moss gives up the liverworts are likely to take over.
Sometimes I wonder if these are worth bothering with. If the conditions are right for growing them then it is unlikely you’ll manage to grow grass. They won’t spread into sunny or healthy lawn areas so leaving them alone is the first option.
If you do want to get rid of them then the best way is to slice them from the soil surface with a spade or rake them up. Thoroughly rake and spike the soil afterwards to improve the soil and prevent the liverworts return. Finally, using ferrous or iron sulphate next time you treat the lawn is worth a try.