Alguns trechos interessantes sobre o tema:
The Balrog is a survivor from the Silmarillion and the legends of the First Age. So is Shelob. The Balrogs, of whom the whips were the chief weapons, were primeval spirits of destroying fire, chief servants of the primeval Dark Power of the First Age. They were supposed to have been all destroyed in the overthrow of Thangorodrim, his fortress in the North. But it is here found (there is usually a hang-over especially of evil from one age to another) that one had escaped and taken refuge under the mountains of Hithaeglin (the Misty Mountains). It is observable that only the Elf knows what the thing is – and doubtless Gandalf.
Fonte: Cartas 144.
Nas palavras do próprio Tolkien, Legolas sabe que o inimigo é um balrog. Legolas também mostra, no trecho abaixo, que a história dos balrogs (no plural de propósito) é conhecida pelos elfos:
"It was a Balrog of Morgoth," said Legolas; "of all elf-banes the most deadly, save the One who sits in the Dark Tower."
Fonte: The Fellowship of the Ring, The Mirror of Galadriel
Pode existir alguma evidência de que a existência de um balrog na Terceira Era era conhecida pelos elfos?
Thus they roused from sleep a thing of terror that, flying from Thangorodrim, had lain hidden at the foundations of the earth since the coming of the Host of the West: a Balrog of Morgoth. Durin was slain by it, and the year after Náin I, his son; and then the glory of Moria passed, and its people were destroyed or fled far away.
Fonte: The Return of the King, Apêndices, Dúrin's folk.
Então há anões sobreviventes, de modo que eles poderiam ter passado a história adiante.
Eu li em The Encyclopedia of Arda (e tem a mesma informação no Tolkien Gateway) que:
In the year III 1980, they dug too deep, and unleashed a nameless terror from the depths beneath the city. The creature wreaked dreadful destruction, and in slaying the then King, Durin VI, became known as Durin's Bane. In the following year, Durin's son, Náin I, was also lost, and the Dwarves fled their ancient home. After millennia as one of the richest cities in Middle-earth, Khazad-dûm stood dark and empty, but for the brooding menace the Dwarves had released. In that time it was given a new name, Moria, the Black Pit.
Essa seria uma evidência de que os elfos (em especial de Mirkwood) souberam sobre o balrog através dos anões sobreviventes. Só que eu acho que a informação está errada, já muitos anos antes do despertar do balrog, os elfos fizeram o portão ocidental chamando o local de Moria:
"The words are in the elven-tongue of the West of Middle-earth in the Elder Days," answered Gandalf. 'But they do not say anything of importance to us. They say only: 'The Doors of Durin, Lord of Moria. Speak, friend, and enter'. And underneath small and faint is written: 'I, Narvi, made them. Celebrimbor of Hollin drew these signs.'"
Fonte: The Fellowship of the Ring, A Journey in the Dark
Estranhamente, no entanto, é dito que:
A maior de todas as mansões dos anões era Khazad-dûm, a Mina dos Anões, Hadhodrond no idioma dos elfos, que mais tarde nos seus dias escuros foi chamada de Moria;
Fonte: O Silmarillion, Dos Sindar
Enfim, é possível que:
1) A notícia do balrog de Moria tenha se espalhado pelos anões sobreviventes;
2) Legolas soubesse dos balrogs através das histórias dos Sindar;
3) Legolas tenha visto através da forma física do balrog, reconhecendo um espírito deformado.