With all proprietary feeds, the only thing that is different is the balance of nitrogen, potassium and other trace minerals. In general, nitrogen aids leafy growth, while potassium encourages flowering and fruiting.
I would certainly use up old rose fertiliser with lilies, but the main thing to remember is that the leafy growth THIS year is what forms the flower buds for NEXT year in the bulbs. So a quick fertiliser applied now will do nothing to improve flowering this year.
Sadly we all usually neglect our bulbing plants once they've flowered, which is the very time we should be looking after them if we want a good display next year. As soon as your lilies finish flowering, give them a little feed, check the leaves and stems to squash the little red lily beetles or the grubs on the leaves, and keep them weed free until they die down in the autumn.