Cut off the long flower stalks and leave the leaves alone - they will be feeding the bulbs for next year. You might give them a potash feed such as tomato fertilizer to help next years flower buds to form. Most lilies will be OK in the ground as they are planted quite deep anyway.

Stera, I have got to move some enormous lilies from my late sisters garden, quite soon. Should I attempt to dig them up with their 4ft stalks attached and replant them in my garden?

I don't know Cammomile. If you have no alternative and if it was my problem I would cut off the flower stalks and leave the leaves as above but have never done it so hope somebody else can you give you more reliable help.
Pity you can't leave them a few weeks longer.

If you can leave them a few weeks until the leaves have died off that would be good. If you have to move them earlier, then so be it and cut the stems off. As you describe these as 'enormous lilies' then you may find that the original bulbs have multiplied up into many and have made a huge dinner plate matt of bulbs. I once lifted a Lilium pyrenaicum, had trouble lifting it into the wheelbarrow and then divided it up into scores of new bulbs that are now located all around Scotland! Hope you are as lucky.

Wow!

I don't think she planted them more than a couple of years ago. They flowered on 5 to 6 ft stalks, lemon flowers and she called them tree lilies. We are in the process of renting out her house and I'd like to keep them as they are so beautiful.

Seen pics in catalogues - they sound terrific!