I would choose one or the other. "Heavy" lifting is subjective, but if it is as heavy as it needs to be to continuously put on muscle, then you need to eat too much to be concerned about your cardio and whether or not you look cut. So to answer your question, yes if you do too much cardio you could very easily over train which is why most body builders go through macro cycles of bulking and then cutting instead of trying to do both at the same time. For every person in the gym with the genetics of Jesus Christ there are 50 that cannot do this.

That said, if you are concerned with cardiovascular endurance for purposes of athletics, I would do do a 20 minute session of HIIT and scratch whatever else it is your are doing. I don't run on the treadmill because I have bad running mechanics, so I use the bike. I go at about 80% for 4 minutes and 100% for an entire minute for 20 minutes.

Surely you can alternate between one or the other, but if you're trying to get stronger I would just pick one and if I were you it would be the HIIT. I'd also make sure to do it after lifting, THEN take your shake.