Is there a train from Dali to Lijiang? How long does it take and how much is the fare?

Yes, there are several normal trains every day. It takes 2 to 2.5 hours on the way.
The ticket fares are in the following: Soft Sleeper CNY111.5, Hard Sleeper CNY77.5, Soft Seat CNY49, Hard Seat CNY34.
The schedules are 05:16, 06:01, 06:19, 09:25, 15:36, 16:19 and 17:27. For more details, you can search the train page of this website.