I too, among many others, am heading to LP as my first IM challenge. I was up there a few weeks ago and the hill back into town is steep. I am considering walking up it on the first lap so as not to redline too early. Part of my logic is that I'd rather walk it the first time than the second, and the overall benefit of walking it the first time would help me on the next 15-16 miles. For reference, my straight up 1/2 marathon is ~ 3:20.

Any thoughts on this strategy?

If running the hill back into town will take you out of your aerobic zone, yes it would be a good idea to walk it. Keep in mind on race day that hill will be lined with people like a mountain stage at the TdF. So if your plan is to walk it. Don't get sucked in by the people trying to get you to run (BTW they are just trying to help). Especially if it will spike your heart rate.