You certainly can grow lemons indoors in the UK, people were doing it a long time ago in orangeries. If you want to try something more ambitious have a go at a pineapple or banana tree, both have been grown inside in the UK.
Regarding the lemons you need to get your humidity between 30-60%, houses are often way below these levels. You can increase room humidity by placing shallow pots of water in direct sunlight in the windowsills of the room that you keep your lemon plants.
Because you are growing from seed you could end up with a very large lemon tree, most of the lemon plants that you buy in British garden centres are dwarf varieties and will never grow more than a few feet tall. The lemon that you obtained the seeds from probably came from a tree that was 20ft tall.