I have a love hate relationship with alstromerias.
I planted a few "special" hybrids with royal names. They grew, flowered amazingly for ar least 4 months non stop. Real eye catchers. However, they suddenly go dormant in mid to late summer, depending on when they started to flower (from early May in my case). This then leaves a large bare spot in the garden for several weeks. They all invade though.
I dug up all my alstromerias but replanted my favourite, Queen Elizabeth (I think) in a location that can be seen when in full flower (5' tall or more) yet disguised when flowering is over. Stipa gigamtea, heleniums, acteas, the Bishop of Llandaff dahlia and a yellow dogwood grow around it. The gap is then not seen.
The orange alstromeria is a thug as Bookertoo and hogweed have said. Don't grow this one folks.
My Queen Alstromeria is now opening a few flowers but I will restrict its expansion.