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I'm in Tbilisi for the past few days, so could check it here. I asked around in a few currency exchange places - and none of them accept foreign coins, lira or otherwise. One of the places suggested that TBC bank branches may be able to exchange coins, however I didn't manage to get to a bank.
My advice would be to take the lira coins with you and head straight for a bank branch. While the exchange rate isn't as favourable as in independent exchange centres, at least you may stand a better chance.