The version I learnt from an elderly lady,as a child is much the same as those above. Always including the lallala's

I love to play my old banjo
I rest it on my knee
But now the strings have broken down
Well it's no good to me.

I took it to a menders shop
To see what they could do
They said the strings have broken down
And it's no good to you

I took it to another shop
To see what they could do
They fixed the strings and said to me
Here, it's as good as new

I love to play mt old banjo
I rest it on my knee
And now I've sung my song to YOU
Well, you can sing to me.

I'm in my sixties now, and I learnt this about age 4/5. I'm also Australian.