During hot summer weather, friendship lilies can develop leaf scorch. This disease occurs when plants can no longer soak up water. Paradoxically, if you give plants too much water, they can also develop leaf scorch. Boggy soil prevents root growth, so overwatered plants fail to take up water. Leaves turn brown, then black. They shrivel and die.
Impatiens necrotic spot virus (INSV) can affect many plants, including friendship lily. INSV's many symptoms include yellowing or browning of leaves, black leaves caused by stem cankers and stunted growth. This disease is common in greenhouse culture, so if you purchased your plant, it could have come into contact with the disease.
Alstromeria are fast growers and will thrive even without fertilizer. If you do fertilize the plant, giving it too much fertilizer can cause leaves to turn black. The excess fertilizer burns the plant.
If your lily has been overfertilized, do not fertilize again for quite some time. Going forward, give only as much fertilizer as directed and do not apply it directly on the plant or to the stems, since that can burn. If your plant has leaf scorch, cut off the blackened tissue. Give the plant adequate water to spur new growth. For INSV, remove affected plant tissue and look for thrips, an insect pest usually found in conjunction with the disease. There is no fungicide for treatment, but you can manage thrips with insecticide. The plant may recover.