For those not familiar with American traditions --

The first automobile produced by Henry Ford (the Henry of this song) was the Model T, begun in 1909. The Model T was known as 'the tin Lizzie.'

(I wonder if Lizzie was a common name for a horse.)

In 1927, the Model T was upgraded to the Model A. The song says that Henry (Ford, the automaker) has upgraded the humble tin Lizzie, and now Lizzie's a lady - i.e, the Model A.

There are hobbyists to this day who keep cars like these running.