Last year I had to go from the law building to Chemistry, it took me precisely 10 minutes to get between those buildings walking at a fast pace. Given that Grattan Street is closed off for construction works, you won't have to wait at the traffic lights which is an improvement!
If I were you, I would leave the lecture at the ending time i.e. a 10am lecture, leave at 10:55 like usual, even if you miss some information you can always rewatch the recording. Of course, if the lecturer is giving you exam info or something I would stay a tad later and be late for my next class.
If you second class is the same subject as your first, the tutor/lecturer will appreciate that a lot of people will be running late. Additionally, tutors/lecturers rarely care if you come in late, as long as you sit down and get your things out quietly.
If your second class is say a small tute or seminar, you could let your tutor know that the reason why you might be late every week is because of your previous class and they should be fine with that
Otherwise you could buy a boosted board (google it) and get there in no time
