How many hours from Lijiang to Lugu Lake & Lasi Hai, what's the temperture there in Jun

To Lugu Lake, the bus will take you about six hours to seven hours.
For Lasihai, I am afriad that there is no such a place, but I know Lashihai, which is not very far from Lijiang. I think you may refer to it. To reach Lashihai, there is no direct bus and you may need to rent a car with other people, which will take you about an hour to reach.
Generally speaking, the temperature is around 15 to 25 C and the temperature difference between morning and night is very big, so I advise you to take T-shirt as well as sleeved clothes.