Does the word "luve" mean "love"?

The short
answer: Yes.

Standardized spelling is something very new to the English
language, as strange as that may seem to us. Go back just two hundred years or so and you'll see
people spelling words all sorts of ways. There wasn't the standardized educational system that
we have today, and there were far fewer dictionaries and other sources that we now turn to when
we want to check the "correct" spelling of a word.

, the author of
the poem you name, lived from 1759-1796, toward the end of the stage of English known as the
Early Modern Period. By this time, a standardized spelling had pretty much already been
developed and disseminated, at least to the middle and upper classes, but it wasn't identical to
our standardized spellng today.

Here are some words from his poem paired with
a modern (American English) spelling:

luve =
love

melodie = melody

weel = well

On a final note, I don't have much proof to support my claim, but I
believe that Burns did not write his poem in the way that he actually would have spoken in
everyday life. He uses the word "thou" in the poem, for example. The
word "thou" had already pretty much been entirely displaced by "you" and
become a fossil by the time he was writing this poem.