First of, LOT does NOT have any IL-62s in service. In fact, they were the first Eastern European airline to go 'all western'. If you doubt me, check out the following link:
Second, you could'nt possible re-engine an IL-62 with a JT8D-200, there's like a 5,000-10,1000 lb thrust difference between the JT8D and the D-30. Maybe CFM56, but not JT8D. But you'll never be able to get two CFM56 engines in tandem on the back of any aircraft, they're simply too big.
I agree with MEA-707, it's cheaper to lease a newer type then to overhaul an oldie like the IL-62. Heck, you could probably pick up an older 767-200 for less then the price of overhauling an IL-62!