You get away with this because of doing low-weight, high-rep work. For somebody trying to get stronger by lifting heavy, your advice would not be so good. I suppose an easy spin in the morning and lifting after work would be OK, but riding within a few hours before lifting is not the best approach if doing a more traditional strength routine.
Uh, no. I've always lifted to failure, which is what counts. I used to do sets of 30, now during the season I'm doing 2 sets of 5 hopefully or else I rep it out to failure, maybe 7 if I've guessed wrong for that day. No difference in biking before or not. I almost always bike about 20 minutes before I lift. Works great. I don't think I'm any stronger now that when I did 3 sets of 30, but 2 sets of 5 sure takes a lot less time and takes less out of me. I work harder on the bike in summer, so the next day's performance matters more.
It's funny how so many people know so much about something they've never done.