Giving an opinion here is like playing in a minefield.
First, my statement about any Ithaca doubles made prior to the New Ithaca Double still applies.
A checkout by a good smith is called for.
A couple simple checks may help here though.
Take off the forearm while the barrels are locked shut. Grab the barrels in one hand and the wrist of the stock in the other.
Twist. If there's movement, pass it by.
Then, reassemble.
Open the action and place a single layer of clear tape like Scotch tape across the breech covering the firing pins.
Close the action. If it locks shut on the tape, there's headspace issues.
And the Ring Test. Dismount the barrels fro0m the rest and hang them off your finger by the lug underneath. Tap the barrels with a non marring tool like a pencil. Any sound made should be a clear ring.
Buzzes and a dead thud mean the barrels are coming undone from each other. Pass it by if so.
HTH.....