Might it work, to turn the plant so that the canopy faces away from the sun, so the bare side faces the sun, to encourage it to make new growth on the bare side? Then leave the plant situated that way for some months, to give it time to respond to the new direction for the sunlight?

I know how slowly grows the kaffir lime my mil has; the citrus forum might tailor an answer better fitted to a lime tree.

Thanks merrybookwyrm i had the same thoughts as you so it has been like this since April last year but as of yet no affect but maybe ill just have to wait and see how it turns out in the next few years.