How big, tall is it, Alma? I mean is it physically possible for you to do this keeping the roots in tact?
What kind of lime is it? Off hand I'd say you could lose a growing season but that it's "possible" to move it. Not sure I'd trim it back. If you go through with this I think I'd be sure to use a lot of new shrub and tree soil and vitamin B to stimulate root growth.
FYI my Key Lime was very badly affected by the hail storm Oct 5 2010. It usually produces in summer. Depending on when your tree produces I think I'd attempt transplant when it finished it's fruit and prior to new flower sets.
