Think we might see the Prodigy characters on Lower Decks?

[Deks]

Prodigy is aimed at children. Lower Decks very much isn't, with lots of adult, very kid-inappropriate jokes.

That's probably the biggest issue.

I don't think Prodigy has ever been referenced in any other shows so it won't change much. I imagine there aren't any legal barriers to using Voyager characters that have appeared like Janeway again as long as they don't mention anything Prodigy-specific.

They could mention something about Chakotay's upcoming mission to the Delta Quadrant and the Protostar class as an experimental ship (since LD takes place before PRO).
But that would likely then necessitate Janeway's or Chakotay's appearance on LD (or both?).

Otherwise, I don't see LD referencing Prodigy, unless there's another time travel event at some point which allows the crossover to occur.

Aside from that... the only other show that could reference PRO would be Discovery in its 5th season... if they find a reason to (perhaps a callback to the Proto Warp propulsion and that SF found a way to make the Protocore main power sourc which can now power its own containment - eliminating the need for M/AM and Dilithium - after 800 years, you'd think someone would look into this).

 

[fireproof78]

Not if someone died.

Hell, Starfleet didn't even pursue the Warp 10 tech because it turned people in to salamanders which was easily fixed.

 

[Oddish]

But that would likely then necessitate Janeway's or Chakotay's appearance on LD (or both?).

Maybe the Cerritos gets an early version of the Training Hologram, allowing Kate Mulgrew to put in an appearance.

 

[Tuskin38]

Aside from that... the only other show that could reference PRO would be Discovery in its 5th season... if they find a reason to (perhaps a callback to the Proto Warp propulsion and that SF found a way to make the Protocore main power sourc which can now power its own containment - eliminating the need for M/AM and Dilithium - after 800 years, you'd think someone would look into this).

The proto-core required an exotic matter dilithium matrix.

 

[Deks]

The proto-core required an exotic matter dilithium matrix.

At the time, SF probably used exotic matter Dilithium matrix as part of it because Dilithium was the primary method of stabilization and a part of power production when the Proto-drive was conceived.
There is no reason to think that would have to remain the same after 800 years (though I'm sure Trek writers would inject that bit of stagnation into the premise to prevent UFP from deploying proto warp on a large scale - which is probably what they did, and hence why Burnham flippantly said that 'no other methods proved viable').