Yes, always let bulbs die down naturally, and please don't torture them by tying up their foliage. Some gardeners used to do this to make old foliage look tidier, but just be patient as they're actually feeding teh bulbs that will multiply and build-up to flower is future years.
Like lazy gardener, I alwasy pick off the old faded flower heads to prevent them wasting energy forming seed heads. Just pick off teh head, leaving the stalk to die down in its own time.
However, unlike lazy gardener I prefer drenching soil around clumps of established bulbs with a generous watering can or two of a liquid feed solution, as this gets straight to work. If conditions stay dry there's a chance that pelleted chicken manure will not dissolve and reach the roots, and won't be of any benefit to the bulbs at all.