250 Fahrenheit is 121 Celsius. This is well above the boiling point of water, thus you have extensive evaporation from the sauce and the sauce reduces to the point at which it can burn - this will be the point at which boiling no longer causes in effective mixing of the sauce due to thickness of the sauce and results in localized heating of the sauce to temperatures above that of the boiling point of water, at which point it can burn.
Leaving the lid on retains at least a portion of the steam and hence returns water to the container, meaning it is thin enough for boiling to prevent localized heating. This means that the temperature of the sauce can't get much above 100 C and no longer burns.
I don't know what temperature in a steam table relates to what temperature in the dish, but it is obvious to me that over time something retained at 250 F (121 C) should (in physics) eventually end up at 250 F (121 C) (though this would be after all the water has evaporated).
In terms of food safety, so long as the dish is above the temperatures recommended by your local food safety authority (e.g. FDA for the USA). For a sauce such as spaghetti sauce (Bolognese?), I would recommend that it is boiled for at least 5 min in the kitchen during preparation (or reheating if prepared prior), then maintained above 165 F (74 C) during serving - see this chart for safe minimum internal temperatures. You might consider Bolognese sauce either a casserole or a ground meat for that table.
You might have to experiment with your steam table to achieve a temperature which will maintain the food at or above this temperature, but a manual for it might well have temperatures to set for different food types to maintain food safety.