You are right in that Tupolev has already tried and tested am LNG powered Tu-154. It's designation was the Tu-155, and made some 100 test flights from 1988.
During testing, it was found that only minor adjustments to the rates air intake and fuel supply had to be made, and that the aircraft was actually cost-effective.
After the testing, it was decided that production of the aircraft would go ahead, using the designation Tu-156. This was to have happened in 1996, but lack of funding pretty much ensured the project never went ahead.
Another problem which affected any production of the aircraft, was the installation by Gazprom at airports, the necessary equipment to be able to refuel and service the aircraft. This would be an immense cost.
There have since been other plans to produce LNG fueled aircraft; the Tu-206 and the Tu-136.
The Tu-206 is basically an LNG fueled Tu-24, and the Tu-136 was to be a development of the Tu-130 (a project that never got off the ground).
Once the Russian economy gets back on it feet, it is very possible that Tupolev, Gazprom and other parties may very well resume studies into the production of an LNG fueled aircraft.
Some information on the Tu-155, in Russian is at http://www.aviation.ru/Tu/Tu-155.html