Is there short term luggage storage at Lille Europe or Lille Flandres?

1) Yes. It is ~10-15 minute walk between the two stations.
2) Baggage storage - don't know.
There are a number of eateries facing Lille Flandres (which is the older station). The old town starts at Lille Flandres, so you don't have to go much further to find somewhere to while away 1-2 hours. You won't have much longer, especially if you have used time to eat.

Hi Ashley
The man in seat 61 has answers to your questions,
https://www.seat61.com/stations/lille-europe.htm
It seems you won't go hungry with the eateries etc at the station. As Lille is an important Eurostar stop and hub for people making connections eg to cross the Belgian border, I would be very much surprised if the town shuts down even if it is a religious holiday. Small French towns are interesting to wander around and you have three hours up your sleeve. Enough time to find a small cafe for lunch and then be back to catch your connecting train at the Flandres station.

Wow, thanks for the quick & very informative responses 👍
I found it funny that the man in seat 61 recommended the Irish bar.... Ive always saidthat wherever you go in the world, you can always find at least one of 2 things: an Irish pub and /or an Australian !
Cheers!
Ashley

There is left luggage at the Lille Europe station. https://www.gares-sncf.com/fr/gare/frlle/lille-europe/services/237/services-aux-voyageurs/bagages#service-177

Two hours is enough for walking through Rue Faidherbe to the two main squares in Lille and exploring the narrow lovely streets with lots of eateries there. I wouldn't miss that.