Lilies generally start to bloom in late spring/early summer when the nights are cool and when the days are getting longer and warmer. Lilies are commonly split into two main groups: asiatics and orientals
Asiatic lilies are the first to bloom in may or june and they are very colorful with bright drastic colors: red, yellow, orange, purple, etc. these lilies are somewhat shorter than the orientals, e.g. three to four feet vs five to six feet. But usually they have no scent. They multiply readily. It is not uncommon to buy one asiatic lily one year and have four to six blooming lilies a few years later.
The Orientals bloom later in july or september. The flowers are usually larger, have greater texture, and can be extremely fragrant. The colors are more suttle and the texture of the petals tend to be more delicate. e.g. compare a strawberry milkshake, oriental, to a strawberry popcicle ,asiatic, for example. Orientals generally do not propagate as easily and readily as asiatics.
Many people believe that orientals are unsurpassed in beauty. Regal, tall, taking their time to flower, but the show is well worth it. Very large, textured flowers with unmistakable fragrance. Others love the screaming bright - in your face - colors of the asiatic lilies in spring when the the summer garden is still to develop.
There are of course exceptions. You can have asiatics which bloom very late, you have orientals which are not fragrant and which flower very early. There are also species lilies and very particular types of lilies which fall outside the two main groups. One example are the pumilum lilies which are high with a very high number of flowers pointing towards the ground, normally asiatics are upfacing and orientals are up or side facing. Minitaure, pixie, versions of orientals and asiatics also exists.
Tiger lilies are similar to asiatics except they are spotted and can carry lily virus inside them without showing it, like a trojan horse. The two main groups: asiatics and orientals are well established and best known. There is a lot of plants which borrow the lily name. Lilies, orientals, asiatics, pumilum, tiger, etc, are all of the genus "Lilium". Other plants may be known as 'lilies' but really they are not 'true lilies'.
Here are some for examples: Daylilies heremocalis, Calla lilies callas, Canna lilies cannas, Toad lily tricyrtis, Plantain lily hosta, Sword lily gladiolous etc. You may say that they are all 'lily wanna-bees'. A lot of people believe daylilies, canna lilies and calla lilies are part of the lily group. They are fundamentally different.
Stargazer lilies can grow in most of usa without problems and the climate in Massachusetts is not adverse to these. Holes in leaves are likely slugs who loves lilies. You can purchase slug bait from garden centers. Apply in very early spring as the lilies poke their head above ground, and then repeat about every three to four weeks, as long as the lilies are small.
As they grow taller you can stop applying snail bait. I still do it up until mid summer because it is amazing how high the snails can travel on the lilies and because we have other plants which also are attacked.
Lilies tend to get thin and spindly if allowed to grow in too dense shade. If shade is the problem, moving them to a a position with better sun should rectify in the problem. The problem can also be one of care. Lilies are pretty easy to care for, but you need to know the basics. Lilies which you want to come back should be fertilized two to three times during the growing period, in early spring as they poke their heads above ground, just before flowering and finally you can broadcast fertilizer over the ground in early fall.
After the lily has bloomed and the petals start to fall off, deadhead the flower. This is done by cutting the small stalk off which holds the flower to the main flower stem. Sometimes, small green puffy seed pods develop where the flower used to be. These should also be removed to preserve energy in the bulbs and avoid the lily spending energy on setting seeds.
Otherwise, leave the main flower stem alone. Many people mistakenly cut the flower stem back to the ground after flowering which removes the potential for the lily bulb to recharge for the following year. The lily needs the flower stem with it's green leaves to conduct photosynthesis, e.g. to recharge the bulb for next year's bloom.
A topdressing around the base of the plant every year with a good quality compost is also recommended. Fertilize two to three times per year. Deadhead spent flowers by removing the dead flowers plus seed pods. Do not restrict foliage, but allow the lily to grow until it turns brown on it's own in fall. If planted in too deep shade, move to a place with more sun. Apply a good layer of compost around the base of the lily in spring and fall, if possible.. optional. This would depend on you and what you think would be best for your lily.