'Near the sea' and 'the Lake District' don't exactly match up very well. Do you want to be by the sea or by a lake? Whichever it is, this website should help:
http://www.ukcampsite.co.uk/
I suggest searching by county, on 'Cumbria'. That will bring up 5 pages of results. Look through them for the sites with a motorhome symbol. You'll find detailed descriptions, together with loads of reviews from users. (Assuming that your motorhome has the appropriate connection - all modern ones probably do - make sure that you look for the words 'electric hook up').
Chris