Any point in upgrading stock cables for a LPS?

Yes, the quality of the power cable on an LPS can make a notable difference. When I had the EtherRegen switch, it wasn’t until I put an LPS with a very good power cable that it made it worth it. I would try on the LPS of the streamer first as it is the most delicate of the two. For streamers and their power supplies, you will hear a good amount of improvement if the power cable’s capabilities have advanced shielding and noise reduction properties. 

Yes, definitely.

My best cables are for Dac, streamer (linear power supply) and amp, in that order.

Then good cables for DDC, network switch (lps), router + 2nd network switch (dual lps), and power conditioner.

Okay cables for Uptone USB Regen, and modem (lps).

Absolutely, yes.

On my 5v LHY LPS for my Node 2. The sound signature of various brands of cords is discernable. I can easily hear the difference between two cords that are the same cord (the no longer available Cable Pro Vitality) but, each of the two has different ends (Iego Gold vs. Oyaide 004). The cord with the 004 ends is clearly better in this case.

Once you adopt the idea that everything matters in your audio system, from the wall receptacle all the way to your speaker footers, then the idea that power cords can be and often are very component and even system dependent needs to be embraced.

A shielded power cable of sufficient gauge for the amperage involved should be suitable. But, if you have extra "audiophile approved" cables laying around then, why not?  Better yet, if you have both then try each and listen for differences.  Once you have it nailed, have a friend or spouse switch them without your knowledge and let us know what you hear.