It's certainly possible for freight and light rail trains to share track, since they do operate on the same gauge of 4 feet 8-1/2 inches. The Federal Transit Administration and Federal Railroad Administration typically require the operations to be divided up by time of day, so freight service would probably have to be scheduled for late at night. That could could certainly increase costs for the freight operator, and would reduce their flexibility a lot.
I'm not sure how common that is, though -- Some examples I know of use diesel-powered LRVs instead of electrically-powered ones like the NCTD Sprinter in the San Diego area, New Jersey Transit's River Line between Camden and Trenton, and then there's the Capital MetroRail line in Austin, TX (which they call "commuter rail" despite using almost exactly the same equipment as the River Line's "light rail" -- though it definitely has a commuter-oriented schedule). However, I've also seen freight spurs along some UTA TRAX lines in the Salt Lake City area, and I believe all of those routes have catenary for LRVs.
The FRA and FTA have slowly gotten a bit more open about the possibility of sharing track between freight and passenger operations -- the NJT River Line was designed with mixed freight & passenger service in mind, but apparently the freight service died off and it was never really used. I believe Austin's Capital MetroRail shares track with freight trains at the same time, but again that's "commuter rail" with relatively infrequent scheduling (half-hourly at peak, hourly off-peak).
For many decades now, the FRA has always been overly concerned with the ability of trains to hold up when collisions happen, though they've always had some pretty kooky ideas about how that should work, more or less equivalent to how automakers thought cars should be built back in the 1950s -- Make the frame really stiff so the train cars will just bounce off each other in a crash. They really should have been working on making signaling systems cheaper and more effective to prevent the possibility of collisions in the first place.
For the tens to hundreds of millions of dollars we're currently looking at for either colocation or relocation, a very good signaling system could be installed on the line. The main problem is that freight trains need 1-2 miles of open track in front of them in order to stop safely. Deceleration is typically limited to between 0.5 (mixed freight) and 1 mph per second (intermodal and unit trains) for freight, but there can be several seconds before the brakes even engage, particularly on long trains -- air brakes need to get filled with/released of air, and that takes time. The amount of time required for brakes to engage can be reduced by adding an extra locomotive on the tail end, or sometimes just an extra rail car with a generator and air compressor system in it.
I think it's a reasonable alternative to consider. And of course if all else fails, the LRVs can stop/accelerate almost instantly in comparison to the freight train, so if an emergency were to crop up, the LRV operator could probably scoot out of the way without much trouble (it requires knowing that the train is there, but LRVs are loaded with cameras and could be outfitted with radar).
Precise schedules would need to be worked out so that the freight train doesn't disrupt LRT operations. Possibly a significant challenge if service is running every 10 minutes, though I think that's just barely doable. And would people care all that much if the line needs a couple of 15-minute gaps through the course of the day?
Anyway, I do want to mention that this is a mainline track, even though it heavily used. It's the former Milwaukee Road transcontinental line to the Pacific Northwest, though large chunks of it have been abandoned out west. I believe Twin Cities & Western owns most of the track between Appleton and Minneapolis, though I believe a short segment close to the Midtown Greenway is technicaly still owned by Canadian Pacific through their Soo Line subsidiary. I believe the Kenilworth segment is owned by Hennepin County Regional Railroad Authority. Twin Cities & Western also has a subsidiary called Minnesota Prairie Line where the track is owned by the Minnesota Valley Regional Railroad Authority, and I believe their operations are subsidized by the MVRRA. I believe the MPL route is a former Minneapolis & St. Louis line.
(I believe I've got to come up with something more creative than "I believe"...)
Here's a quick map I drew up of the system -- I'm not sure how much of the track really gets used on a regular basis -- the Minnesota Prairie Line in particular sees very little traffic, particularly west of Winthrop (only about 1/3 of the way down that line).
The cost to run Northstar on BNSF's mainline with 50-60 trains/day is not especially relevant to this route with a frequency of freight traffic that's 20x smaller. David Levinson did a
back-of-the-envelope estimate of TC&W's market value, and came up with a cost around $110 million for the entire company. He was suggesting a buyout of the whole railroad, though I don't think that's a very good idea.