My guess is this might be related to the IE Anywhere feature (which is turned on by default in LP for Apps).
Unfortunately, we don't get registration events for all new browser windows, so we have to poll. We have added a few new preferences to turn off IE Anywhere and Polling in this version:https://lastpass.com/lastappinstall.exe
Please turn off polling and check if that fixes it. You can also optionally turn off IE Anywhere (although I would suspect that wouldn't make a measurable difference).
Let us know if this doesn't fix it and we will have to debug further.