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The following articles should help: https://www.gardeningknowhow.com/ornamental/bulbs/peruvian-lily/growing-peruvian-lilies.htm
https://www.gardeningknowhow.com/ornamental/flowers/salvia/growing-different-salvia-types.htm
https://www.gardeningknowhow.com/edible/herbs/lavender/pruning-lavender.htm

I think you meant Alstroemeria. It will grow in zone 6-10. Some parts of Michigan are zone 6 while others are 5 or 4. It depends on where you are in Michigan.

This article has more information:
http://www.bhg.com/gardening/plant-dictionary/perennial/alstroemeria/

Do you fertilize these at least once per year? If not, I recommend doing so. It sounds like there is a lack of potassium and phosphorus in the soil.

Here is an article for more information on this plant: https://www.gardeningknowhow.com/ornamental/bulbs/peruvian-lily/growing-peruvian-lilies.htm

Keep the soil moist, as Alstroemeria produces the most blooms with moist soil and may become dormant if the soil becomes too dry. Don't allow the soil to remain soggy, as excessively wet soil causes rot and fungal disease. Water the plant lightly during periods of dry winter weather.

Feed the plant in spring, using a general-purpose, time-release fertilizer. Apply the fertilizer at the rate recommended on the container and water the plant deeply to distribute the fertilizer. Repeat in midsummer and early autumn.
Keep the soil moist, as Alstroemeria produces the most blooms with moist soil and may become dormant if the soil becomes too dry. Don't allow the soil to remain soggy, as excessively wet soil causes rot and fungal disease. Water the plant lightly during periods of dry winter weather.
Divide Alstroemeria during spring, summer or fall if an older plant begins to appear woody, overcrowded, or nonproductive. Dig up a clump and pull the tuberous roots into smaller sections, each with at least four or five healthy roots. Plant the smaller sections in well-drained soil and full or partial sunlight.

Hm... I'm not quite sure which plant you are referring to, exactly. Did you mean Alstroemeria?

If so, then this article will help: https://www.gardeningknowhow.com/ornamental/bulbs/peruvian-lily/growing-peruvian-lilies.htm

This is a Perennial, but they will succumb to overwatering quite easily. This is likely the case, here.

If they do not come back, then they will require a fresh planting.

This article will help you with their care:

https://www.gardeningknowhow.com/ornamental/bulbs/peruvian-lily/growing-peruvian-lilies.htm