I bought my first house last fall, and it was built in the 1950s in the Seattle area. When the home inspector looked at the sewer pipes he didn't note any concerns about the age of the pipes. Recently though, I had a plumber by for a look at the water heater (just a checkup). Anyway, he said he was concerned about the wear in the concrete sewer, because the aggregate is well exposed. Based on the general experience though I got the feeling he was trying to sell his services more than address any real needs (being 60 years old, most of the pipes in the house are undersized by modern code).
Anyway, how long should the concrete run to the sewer last? Should I prioritize putting in a liner, or should it last as least another 5-10 years, when I'll be ready for more extensive plumbing updates.

My experience is with concrete storm drainage/culvert pipes. The wall thickness of the concrete pipes was determined by converting the inside diameter of the pipe to feet, then adding one inch, the result being the wall thickness in inches. Example: 30 inch dia. Pipe = 2.5 feet plus one inch = 3.5 inch wall thickness for a 30" pipe.
If you have for instance, a 3" concrete pipe, the wall thickness by the above system would be 0.25 plus 1" = 1.25 inches (if the formula holds for smaller concrete pipe) and if there is aggregate exposure it is eroding and there isn't much wall thickness to spare.