I used to consistently be able to do T3-T1 International connections landside in 30-35 mins (plane to lounge). That is with IRIS. Arriving flights from the middle east always slow Immigration down to a trickle, even at FastTrack. The walk T3-T1 only takes me 10-15 minutes, and even with a toddler in a stroller we made the walk in 15 mins.