You should follow your doctors recommendations.
Also know that even for someone like me with cirrhosis for the last 9 years I am not on the liver transplant list. Liver transplant is done as a last resort to prevent death. Those people receiving a liver transplant are very seriously ill.
Fatty liver can be a consequence of being overweight there has been an increase of incidence of fatty liver as the US population gets ever more overweight in general.
If being somewhat overweight is the cause of fatty liver loosing some of that extra weight could do you a world of good.
But really you should speak with your doctor.