Let me caveat just a bit.... Whether this a reasonable connection or not could depend where you are in the arriving plane. A TED flight from LAS could be full of folks who have stuffed most of Las Vegas into the overhead bins. If you're mid-to-back-of-the-bus, you could lose 10 minutes (or maybe more) to waiting to get off the plane.

And if you are in the high 80's and have to go to the high 60's, that is a hike, and I'd say it's closer to 20 minutes at a reasonable pace. The golfcarts are a godsend in such situations, but you can never assume one will be available.

In any case, should you combine a 5 minutes late plane with a 15 minute wait to get off the plane with a 10 minute run, well you get the idea..... The CSR's may have gotten itchy fingers at 20 minutes out and your upgrade (assuming you have one) could be gone.

Personally, I have tried never to book a connection of less than an hour at LAX.

But I certainly hope your mileage varies.