  We compute both classical and quantum finite-size corrections at leading
order in the strong coupling limit for the (dyonic) giant magnon in the
Lunin-Maldacena background. Based on the exact S-martix conjectured for the
deformed theory, we generalize the Luscher formula to include twisted boundary
conditions and show that the results match with those derived both by
finite-size classical solutions of the giant magnon and by algebraic curve
analysis.
