Of course it happens, and I am lucky enough to learn lyrics quickly for many songs but am completely awed by two types of performers, the folks who can remember the words they want for huge numbers of songs, and the folks who recover. I suspect the learning of them is in rather a large part the "you do or you don't" situation, but there is no doubt that practice, constant drilling, helps one get better. But the means of improving retention and of recovering are probably learned, often under considerable duress I expect.
My mother took down everything, and I mean everything, in a silent and unwritten shorthand; as a child I noted her right index finger moved continuously through all conversations and even when she was listening to the news or reading the newspaper. This kept her shorthand fluent even years after she had worked as a secretary. I suspect cultivating this habit has helped me, in the way that taking notes helps one remember, even if one never looks at the notes again.
Gordon Bok, in my mind one of the finest ever, loses words rather regularly when performing live, and usually just "freezes" until it comes back. Dave Parry did the same but his freezes were sometimes much longer.
Danny O'Flaherty has a rich Connemara accent and when he loses a word or a phrase he simply leans a bit away from the mike and fills in softly with any syllables that maintain the rhythm; keeping the melody uninterrupted is key. I had enjoyed listening for years before I noticed how often he did this, he is that smooth with it; I just assumed I missed a word or two.
Some start over. Unless this block happens in the first phrase, I find this very distracting. In my mind lilting or otherwise faking it (what are instrumental bridges for anyway?) until time for the next chorus and going on from there is much more satisfactory. Repeating (without disrupting the flow of the song) the previous verse often helps the next one surface as well, and many ballads have a good deal of rather ritualistic repetition anyway, so this solution often works admirably. A good number of listeners don't even notice.
Cultivating the "instant rhyme" can help but may be a trait that you either have or do not.
Flat invention sometimes works, but only on some types of song. I heard a rather well-known singer once start "Seven Drunken Nights" and realize he had not sung it in many years; he made up verses onstage that had us in hysterics. (Whose bum is that upon the bed? It's nothing but a pumpkin. . .A pumpkin with a stem like that I never saw before. . .)
A friend who hits a blank stops cold and says with his irresistible grin, "and that's all I know" and goes straight into something different but similar, generally same key and tempo as well as theme. This works for him but seems very much personality and style dependent. He also often makes on the spot medleys, most well planned but some spontaneous and unexpected (I constantly have an ear out for songs that "go together" but was quite amused to find how easily "The Rattlin' Bog" goes into "Hava Nagilah"). If you mentally "file" songs by key and tempo this could be useful.