Hi karen it sounds like Lucy should definitely be entitled to help with mobility. Have you got the form already? They ask questions like, how many days a week do they need the help which would be 7. They ask 'does your child have difficulties walking' which would be answered yes and then you go on to explain. Harrison has severe hypotonia so can only walk short distances and we need to use his pushchair alot, he can't walk outside without assistance, needs constant supervision etc etc - it sounds like Lucy is similar. You would need to mention about the poor coordination, balance etc. Even though Lucy can walk a little bit you should still be entitled because you would need to carry her alot & use her pushchair.
pm me on facebook if you need any more info, i was lucky that i had help completing mine for Harry and i know it can take a while to answer all the questions. Good luck xx