Consider the rough economics of a diner on the LSL. Staffing is around $160/hr (including taxes and benefits). The staff is on the clock for about 24 hours per run (allowing for delays). So that's $3800 in labor. The energy cost of pulling and powering the diner from NY to Chicago is about $1000. Then the staff have a couple of roomettes, do they not, so you have to look at the lost revenue for two roomettes from NYP-CHI which is something on the order of $600* (allowing for roomettes that go unsold and seasonal variation), plus a likely $50/night for hotel (If Amtrak is committing to 365 room-nights a year (double occupancy) with never more than 2 per night, just about any hotel in the Doublefairhampgardencourtrenaton bracket will happily rent the rooms at $50/night**) on the away leg. So that's $5450 or so in fixed costs for providing the sleeper.
An LSL run has about 8 hours of diner service and maybe does about 30 meals/hour. $5450 over 240 is about $22 that each meal has to charge over and above what Amtrak paid for the food, whether it's a man, woman or child. An omelet+toast+juice (wholesale cost about $3) needs to be $25. Ditto for a kid's hot dog+chips+milk. A steak+mash+veg+wine+dessert (wholesale about $10) is a more reasonable $32 (still pricey compared to TGI Chilibees), but if you can't get $25 for breakfasts or kids meals, we're talking a break-even price of more like $45-50. But you could probably make the diner break even if you took $55 from every sleeper ticket for meals (losing some on 49 and making it up on 48), but that suddenly makes abolishing sleeper service on 48/49 look economically promising (of course, without the sleeper patronage, the diners would pretty soon follow the sleepers onto the scrapheap). Even best case, if you had the diner packed from open to close every meal, you'd have maybe 350 meals a run and be able to cut about $7 per meal, which takes you from outrageous*** menu prices to merely a little bit unreasonable. And of course, the foregoing costs-of-goods-sold assume zero spoilage/shrink.
TL;DR: There is no universe where the LSL as currently run can break even on a diner.
So that leaves open the question of whether the LSL can be run differently to have a more viable diner.
Consider for the moment if the LSL was rescheduled so that 48 and 49 were both day trains west of Buffalo, with 48 arriving around 10 at Buffalo and dropping the diner and 49 departing Buffalo about 5am with the diner. You'd eliminate nearly half of the labor (call it $1600 a trip). You'd save $500 in energy, offset by maybe $200 in switching at Buffalo (maybe that's the second life for the P* locomotives: HEP-equipped switchers and rescue locomotives in Buffalo). You'd no longer be giving up $600 a run in sleeper revenue to provide the staff a place to sleep on board. But there'd be no decrease in meal hours (you'd go from 1 breakfast and either lunch or dinner to 1 lunch and either breakfast or dinner), so this would cut the gross-profit-per-meal target to $8-$12 (350-240 meals per run), which effectively means take $7-10 off every meal, which might actually get some coach passengers to pony up and makes the sleeper->diner allocation go a lot further (though you would likely get more NYP-BUF sleeper tickets; since there would be no dining car for those, it would be unseemly to allocate for those pax).
Similar reasoning would apply to the Capitol Limited (with the rough midpoint being Pittsburgh), though it might make sense to switch the Cap to single-level with the opposite schedule as the LSL and route it via Harrisburg/Philadelphia/Baltimore while moving the Cardinal back to Superliners with a full Superdiner terminating in Washington and timed in Chicago to facilitate the western transfers (wild idea: daily through sleepers from the Builder/Zephyr/Chief with the Cardinal in the summer... brand it as The American: the ultimate land cruise in North America). The Cardinal is the most "western" of the NEC-Chicago trains, after all.
*: I'm including the coach fare, because the general impression I get is that sleeper pax will call an airline if the sleeper's not available rather than travel coach. Also note that this fare is based on the contemporary offering: if the NARP crowd are right that sleeper passengers writ large place a lot of value on the diner, then in the universe where 48/49 have diner service, this cost is more than I've pegged it.
**: The marginal cost for a hotel in that bracket to clean a room, check you in, feed 2 breakfasts, and check you out is less than $20 if they're not swiping a card. Speaking as a former Fairhampyard night auditor, if I had an available room, I was basically authorized by management to go as low as $70/night ($60 if it would mean a sell-out) to keep a late walkin from turning around.
***: I have seen articles musing about how wasteful Amtrak is, given that they charged like $9 a dozen years ago for a hamburger, so the high menu prices have their own toll on Amtrak's image.
