It might be possible to store the lost heat in water and add it back later and even add more heat to it with cheap and simple thermal solar panels which would add (simple) solar energy to system.

Yes its a thermo cycle so there is the inherent loss but your losing energy that would be wasted to add peak power handling capability. Pumped storage has losses also. As long as the losses are resonable and I consider 50% reasonable then it makes sense to add the capacity. Consider the effect of having a several hundred  thousand gallons of liquid nitrogen stored at a wind farm it makes them viable for full load. In the home in the summer the liquid nitrogen can be used directly for air conditioning and also electric generation. Massively reducing the load. Also if you have a home windmill and solar panel your liquid nitrogen storage system means you keep the energy you generate or if you do sell back to the grid you can sell at peak price rates so your in control of when and how much energy you put back on the grid.

In the case of a wind farm or solar array located in the desert when you boil the liquid nitrogen you will be able to condense a fair amount of water from the atmosphere so it also makes it a source of water and of course nice cold air in the desert.

The energy density of liquid nitrogen is pretty high not quite enough to make it a good system for mobile transportation but its really quite reasonable for fixed energy storage.

Finally a co-product would be pure C02 this can be combined with electrolysis of H20 to give you H2 which gives you CH4 and you have a product for organics production.