"Léa would like rather to sleep in a luxury hotel."
Translation:Léa aimerait plutôt dormir dans un hôtel de luxe.
To defend Duo, I sense a difference between 'like rather to...' and 'rather like to...'. The first one would be natural in a context where it followed a statement of different options put to Léa on where she could sleep and this was her preference over the other options (thus putting the stress on 'rather'). 'Would rather like to' could be merely a general statement (with perhaps a touch of British understatement) without any suggestion that other options are currently being considered.
The problem for me is knowing what the French means. Is 'plutôt' qualifying 'voudrait' (which placement after the verb might suggest) -- ie a form of British understatement? Or is it qualifying dormir -- ie she would rather sleep in a luxury hotel than the other things you can do there, like drink in its bar? Or does it mean she would rather sleep in a luxury hotel than, say, in a tent in a field -- which is more like my interpretation of the English discussed above?