Is it appropriate to put Agapanthus under grow lights in the winter? if not, would a dark place in the basement (which is quite warm) be better?
There are generally two species of Agapanthus: the evergreen type (Hardiness zone 8+) and the deciduous type (Hardiness zone 6+). The deciduous type (A. campanulatus, A. caulescens & A. inapertus) dies back over the winter and needs a period of cool and dark conditions. The evergreen type (A. praecox & A. africanus) can be treated as an indoor plant and will continue to grow leaves, and sometimes flowers, during the winter. These herbaceous plants are greatly used in containers, however, due to their cultural requirements it is difficult to grow them permanently outdoor in our climate. Agapanthus rhizomes require very well-drained soil, a full sun location and protection from frost.
I would suggest you try to overwinter it by planting it in a pot with a well-draining potting medium. This will allow you to take the pot indoor in the winter at the first sign of frost. If you have a deciduous one, put the pot in an unheated garage or any frost-free area. Next spring around the beginning of May, you can take the pot outside and place it in a sheltered area so that it can be acclimatized. Cut off any dead leaves, water when the soil dries out. Once you see new green leaves appearing, you can place the pot in a sunny location. Continue watering and fertilizing a month after the blooms finish in order to feed the rhizome for next year’s flowering. If you have an evergreen one, then bring it indoor and place it in a South or West window and treat like any other houseplant. Then, take it outdoor in the spring, after the danger of frost has passed.
Please note that it seems that Agapanthus bloom better when they are root-bound, therefore, only repot when it becomes overgrown and needs to be divided.
As a point of reference, a lot of the hybrids available are cultivars of A. praecox and A, africanus.
Please keep in mind that overwintering tender bulbs/rhizomes/tubers/corms is sometimes a lot of trial and error as each winter is different and unpredictable.