Cut lilies keep better when stems have access to clean water and the vase stands away from heat and direct sun. Follow a labeled flower-food product rather than combining unmeasured household additives.
Start with a clean vase
Wash the vase before arranging the lilies. Remove leaves that would sit below the water line, trim the stem ends with clean tools and place the flowers in water promptly. Keep enough water available as the stems take it up.
Keep the display cool
Choose a position away from direct sunlight, heaters and other sources of strong warmth. Remove fading material and refresh the water and vase as needed. If using commercial flower food, measure it according to the package rather than adding extra to the solution.
Handle pollen carefully
Removing ripe anthers can help prevent pollen stains, but it is not a guarantee of a particular vase life. Handle the flower gently so that pollen is not rubbed into the petals. Avoid mixtures of beer, salt, sugar and vitamin tablets in unmeasured amounts. Cleanliness, water uptake and the condition of the flowers when purchased are more useful things to control than a promised number of extra days.
Related reading: Foxtail Lily Care: Plant Identity, Position and Seasonal Growth.