LOBELIA F1 WHEN LOBELIA HAS FINISHED FLOWERING SHOLD THE BE CUT TO GROUND

If they are F1 I think that is an annual so I'd pull it out and put it in the compost heap. I just googled it at this link and they are saying it is a HHP or HP. Half hardy perennials need to be brought in to a sheltered location which is frost free in winter but a HP Hardy perennial can stay in the garden and overwinter in the ground. If you have to leave it in the earth I would leave the foliage on over the winter and that will give a certain amount of protection from the frost. You could also mulch it using compost or bark over the crown of the plant. http://www.mr-fothergills.co.uk/seeds-plants-gardening/13482/lobelia-fan-mixed-f1