I would say "two consecutive lines." But if I wanted to sound more colloquial, "two lines in a row" is clear and natural.
"Two straight lines" is wrong, for the reason you mentioned. Oddly enough, though, "two lines straight" works perfectly.
It's not a folk rhyme, by the way. It was written by Jane Taylor in 1806. For more details perform a Google search on "twinkle star wikipedia".
Stylistically, I don't myself like the repetition in "Up above the sky so high/Like a diamond in the sky." But repetition is less frowned on in English than in some other languages, and I could cite similar patterns in other poems and song lyrics. The problem for me is that the stars are IN the sky, not ABOVE the sky.
It was written as a poem, and then it was discovered that it fit the tune of a French folk song, "Ah! vous dirai-je, maman." Mozart wrote a series of variations on this tune.
As a kid, a friend and I were interested in science and he taught me a parody:
"Twinkle, twinkle little star
How I wonder where you are;
Up above I see you shine
But according to Dr. Einstein
You are not where you pretend!
You are just around the bend,
And your sweet seductive ray
Has been leading men astray
All these years, O little star!
Don't you know how bad you are?"