I will be going to Lijiang onwards to Dali and Stone Forest and then to Kunming.

Yes, the transportation is easy. Here are some tips.
In Lijiang Coach Station, from 07:10 to 18:30, there are 25 buses available to Dali everyday. The bus varies because of the different condition of the buses. The fare ranges from CNY56-88.
Well, I suggest you reach KM first, and then head to Stone Forest. From Dali Xingsheng Bus Station, there are 23 buses available to KM from 07:50 to 22:00. The bus fare is CNY125 – 137.

In the KM East Bus Station, there are direct buses going to Stone Forest. From 07:00 to 19:00, the bus runs at an interval of 30 – 40 mins, and the bus fare is CNY27.