It seems that the Ring took control over Frodo, and he used it instead of throwing it to lava.
It was destroyed by pushing Gollum, who was holding the Ring, into the lava.
Does it mean that Frodo was not capable of destroying the Ring, and he was just lucky that Gollum was there?
Sort of. There are secretly two parts to the question, each of which have a different answer.
Emphatic yes. Tolkien says as much several times in his letters, but I'm going to quote Letter 191 (emphasis his):
If you re-read all the passages dealing with Frodo and the Ring, I think you will see that not only was it quite impossible for him to surrender the Ring, in act or will, especially at its point of maximum power
[...]
No, Frodo 'failed'. It is possible that once the ring was destroyed he had little recollection of the last scene. But one must face the fact: the power of Evil in the world is not finally resistible by incarnate creatures, however 'good'
The Letters of J.R.R. Tolkien 191: To Miss J. Bum (draft). July 1956
Not really. Gollum just happened to be in the right place, at the right time, at the end of the right string of circumstances. The actual key to destroying the Ring was Ilúvatar, the God of Tolkien's mythology.
The end of the story is a statement of Tolkien's moral philosophy, that salvation and the ultimate destruction of Evil is something that only God can accomplish.
Again, no. Frodo himself caused Gollum to be there, by not killing him earlier in the story; as Tolkien writes in Letter 246:
Frodo had done what he could and spent himself completely (as an instrument of Providence) and had produced a situation in which the object of his quest could be achieved. His humility (with which he began) and his sufferings were justly rewarded by the highest honour; and his exercise of patience and mercy towards Gollum gained him Mercy: his failure was redressed.
The Letters of J.R.R. Tolkien 246: To Mrs. Eileen Elgar (draft). September 1963
Far from being the result of luck, Gollum's presence (and thus his being the instrument of Providence that achieved the Quest), was a direct result of Frodo's earlier mercy, and his (accidental) destruction of the Ring was part of Frodo's reward.
Jason Baker's answer is mostly correct, but I will dispute something: Gollum was key to destroying the Ring, as was shown in a few places.
Gandalf tells Frodo, in The Fellowship of the Ring, The Shadow of the Past, of Gollum:
And he is bound up with the fate of the Ring. My heart tells me that he has some part to play yet, for good or ill, before the end
Frodo remembers this conversation when he finally meets Gollum in the Emyn Muil:
I do not feel any pity for Gollum. He deserves death.
Deserves death! I daresay he does. Many that live deserve death. And some die that deserve life. Can you give that to them? Then be not too eager to deal out death in the name of justice, fearing for your own safety. Even the wise cannot see all ends.
Frodo is wiser than many give him credit for. He binds Gollum to the Ring with the promise, knowing better than any present what it means:
Frodo drew himself up, and again Sam was startled by his words and his stern voice. 'On the Precious? How dare you?' he said. 'Think!
One Ring to rule them all and in the Darkness bind them.
'Would you commit your promise to that, Smeagol? It will hold you. But it is more treacherous than you are. It may twist your words. Beware!'
Then he notes the power he has over Gollum at the Black Gate:
In the last need, Smeagol, I should put on the Precious; and the Precious mastered you long ago. If I, wearing it, were to command you, you would obey, even if it were to leap from a precipice or to cast yourself into the fire. And such would be my command. So have a care, Smeagol!
And at Henneth Annun, he threatens to use this power:
'Smeagol!' said Frodo desperately. 'Precious will be angry. I shall take Precious, and I shall say: make him swallow the bones and choke. Never taste fish again. Come, Precious is waiting!'
Finally, he actually uses that power just before going into the Sammath Naur:
stern, untouchable now by pity, a figure robed in white, but at its breast it held a wheel of fire. Out of the fire there spoke a commanding voice.
‘Begone, and trouble me no more! If you touch me ever again, you shall be cast yourself into the Fire of Doom.’
And then Gollum "touched" (attacked, up to and including biting off his finger) him again.
This may have been "scripted" by Iluvatar, but Gollum was indeed crucial to the Ring's destruction, since, as Jason Baker noted, Frodo was not capable of destroying the Ring himself.
