Lavender in Containers in Zone 5

I'm planning to start growing lavender in containers on our patio. I hesitate to plant in the ground right now as we have some construction going on in the yard and also have a large dog who keeps digging holes. At the moment, containers seem the safer route. I've ordered several plants and seeds to start at home. My concern is that I would like to keep the plants from year to year and I'm not sure how to do it. We live near Boston (zone 5) and the past few years have had at least one very brutal cold snap (-15F) or so. I don't have enough window space indoors for the number of plants I'd like to grow. Should I gather the containers in a sheltered area in early winter and mulch around the pots with straw? or try to bring them indoors in the "shed" where they won't get much light if any light? Do I need to bring them indoors and keep them under grow lights all winter? What is the best way to proceed?

You won't be able to leave the containers out of doors in the winter, because the roots would experience a zone 3 winter out of the warming soil and the hardiest lavenders can only survive zone 5.
Mulching will help a bit, but unless you supply a very heavy mulch, blanket, plastic sheeting, etc, it won't make enough difference. The best would be to dig the plants pots and all into the soil for the winter and then mulch them to make up for the restricted root run. They should be just barely moist before covering, to prevent rot.
The shed may be OK. They won't need much light as long as they are near freezing, as they will be dormant. As long as the shed stays substantially warmer than the out of doors, but also does not go too far above freezing, since the roots again will get as cold as they would in the soil two zones colder than what they are experiencing.
If you choose the under lights option, the plants are not going to do well unless you keep them about 4 to 5 degrees Celsius (40 to 45 degrees Fahrenheit), on the dry side and as bright as possible -hard to do indoors.