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The cry of Morgoth in that hour was the greatest and most dreadful that was ever heard in the northern world; the mountains shook, and the earth trembled, and rocks were riven asunder. Deep in the forgotten places that cry was heard. Far beneath the ruined halls of Angband, in vaults to which the Valar in the haste of their assault had not descended, Balrogs lurked still, awaiting ever the return of their Lord; and now swiftly they arose, and passing over Hithlum they came to Lammoth as a tempest of fire. With their whips of flame they smote asunder the webs of Ungoliant, and she quailed, and turned to flight, belching black vapours to cover her.
It doesn't actually say anything about how fast they got there. "In that hour" simply means "at that time" here. On the other hand, they travelled "as a tempest of fire", which certainly implies magic and speed. Either way, with such inherently magical creatures as the Balrogs, saying that they cannot travel very quickly without flying seems somewhat naive.
Good meme though, always appreciate something that makes me go back to the scriptures.
they arose, and passing over Hithlum
To me, this implies some form of flight, since they passed over, rather than through some place.
It could also mean they trampled over it, destroying it in their wake, thus going over it without flying, so to speak
I mean no, they arose from their hiding in the depths of Angmar is definitely how I'd interpret that