For Lithuania, the best chance for pagan religion to survive would be for Ogadei Khan to send Oirats, who are already Vajrayana Buddhists instead of Khalkas, who are pagans who later, under Birkai Khan, convert to Islam, to conquer the West under Batu Khan and Subotai (which would make an excellent TL BTW).
As vasp said, Mongols didn't showed a great missionary enthusiasm, not really caring about religion except if it was a drive against them.
It was due to some factors as a really simple diplomatic policy (that you can summarize as "Bow or Die" and even Muslim Mongols (that should have a more important conversion drive) had many Christians vassals without searching to convert them.
The problem isn't to have Buddhists among the invaders, you had OTL among the Blue Horde or even to have the leaders of the Horde being such (Ögedei Khan, however, is indicated as a follower of traditional Mongol rites and more being the usual almost syncretist ruler rather than Buddhist).
It is to have Mongols having an interest to use a religious policy that is most likely to divide themselves and to unite their vassals against them.
I can't find a good example of religious conversion made by Mongols (it would most likely be the contrary) and I wonder if a Khanate spawning on more Christian lands than OTL couldn't have ended using a very original (and heretical) version of Christianism.
One thought. If she stays Pagan another century or so, might Lithuania then adopt Protestantism instead of Catholicism?
It would have meant no Poland-Lithuanian union, and having a likely war against Teutonic Order in a far less good position : I wonder how much it would butterfly Torun Peace.
Assuming all the consequences didn't prevent the surviving of Lithuania as independent...It's possible, but as much as Catholicism or Orthodoxy. (If they focus as OTL on the Polish alliance, Catholicism seems still more likely)
Perhaps if some King unified the Lithuanians 400 years early, then reformed their Romuva Faith like in CK2.
And this king would have married the daughter of the viking kingdom of England, his dynasty managing eventually to become the pagan rulers of HRE. Before the conversion to EUIV allowed them to conquer the Aztec Empire, of course.
It's not because CKII implemented "reformed pagan" in order to make Pagans look less miserable compared to other religions that it could have been plausible.
Now your idea of uniting Lithuania and/or neighboring Baltic people is a good one : but in the IX, there isn't much incitative to do so.
No powerful neighbor, Carolingians, Byzantines or Khazars are too far to be an influencing factor (as they were for respectively Western Slavs, Balkanic Slavs, Russians statelets)...A Baltic leader could have managed that, but I don't see why his dominion would have effectively lasted after his death.
Baltic people uniting themselves, not against western pressure, but Rus' could be more easily reachable and less isolated with the presence of pagan neighbors (Pomeranians, some Scandinavians).
However, these having little contacts and being largely distinct paganism, I honestly don't see how it could durably resolve the OTL issues : if something, the conversion of Lithuania could have been more easily hastened than delayed.
No Teutonic Order could do the trick, but I wonder if they couldn't have been replaced by Christian Scandinavians.