There are probably multiple things going on and they are different issues between the summer use and winter use.
First, on the ice, if you remove the transducer out of the hole and move to another hole, you should really “stop sonar” before removing it. If you don’t the transducer is pinging into outer space and has trouble when you put it back in the hole. This same thing would apply if you had your sonar unit connected to a trolling motor with a transducer in the head of the trolling motor and you pulled the motor out of the water.
I know it seems odd because you can pull the transducer out of the hole with various Marcum/Vexilar units and never have an issue, but trust me, try stopping the sonar on the lowrance and I bet that issue goes away.
Second, depth reading in your boat is inconsistent at higher speeds. This most likely has something to do with its mounting location. You must have rivets, rails, etc creating turbulence and that will cause issues. Also make sure the transducer isn’t mounted too low. It should be barely below the hull of the boat, maybe half the height below the hull. Much farther than that its just going to collect a ton of debris and also cause turbulence giving you poor readings.