combining HITT and starting strength

[Wynton]

As many of you know from other threads, I've been inching towards some lifting, and now finally see on the horizon the ability (i.e., proper instruction) for the basic starting strength lifts. The remaining question is scheduling.

Currently, I play tennis two mornings a week (Tuesday and Friday). I am able to get to the gym both weekend days and one other weekday. On those days, I've been going 30-60 minutes on an elliptical, with an intense 20-30 minutes of that time on an interval program.

In order to incorporate the recommendations of starting strength (3 nonconsecutive days of lifting per week), I will either have to cut something out or combine activities.

Is there any reason I couldn't combine my time lifting with my time on an elliptical on one day? If I do, am I correct in assuming that I should lift first?

Also, how long should I expect starting strength to take at first? Since it's only 3 lifts a day, will this take longer than 20 minutes or so? If it really goes that fast, then perhaps I can get to the gym more frequently, avoiding the need to combine activities.