Gollum exiting Moria

[Secret Fire]

Then again, he could always take the endless stair, walk to the top and climb down the mountain. The Fellowship tarried in Lorien for some time...

No, that is not quite possible as the only way Gandalf got to the endless stair was by falling down the abyss and following teh balrog, and it went from the lowest chamber to the highest peak, but it is entirely possible that since there was such a following on the fellowship by orcs that Gollum was able to follow them out, they would know the many ways out, and also trolls were bridging gaps with planks. Anyway, he could have followed the orcs who were intimately aware of the passages in Moria.