Hi,Law
There are more rain in July and August than in other months in Lijiang. You should bring rain gear along.
As for the transportation, there is no direct train between Lijiang and Chengdu. You have to transfer with trains or with train and buses, which is kind of troublesome. So i suggest you take flight. Check this page to see whether there is cheap flight available: https://www.travelchinaguide.com/china-flights/