what sort of LCD ? what is its current drain ? maybe you are asking more of the regulator than it can handle ?
if the inductor ( and its the correct one for the cct) is getting hot, thats inferring a large current flowing through it
What is the part number of the inductor?
Also, what is your maximum input voltage?
If you measure the efficiency you can tell if the inductor is saturating. If the inductor saturates, it will cause all sorts of problems.
When an inductor saturates its core domains are all flipped so there are none left to flip. At that point it acts like a big resistor and eats up power. This is easily detected on a scope with a current probe as a big spike in current, but also shows up as decreased efficiency by quite a bit in most cases. An inductor with a larger core would solve the problem, and this would be one with a higher saturation current rating.