velpremus,
I sent an email to the South Lanarkshire Archives just this morning, explaining what I was trying to find out, so I am hopeful that this might lead to some useful information. The place in question is Lesmahagow, and I gave them the address. Besides enquiring about who owned the house before as well as when my grandmother lived there, I asked about where I could find the Electoral Registers for that area, and I also enquired if they would do a look-up regarding this.
neolithic,
I used to be a member of the Lanarkshire Family History Society, and I still sometimes have a look at the site as a guest. I may contact them. I could post a message on their public forum, or enquire directly to their Motherwell offices.
Graham,
I have never actually managed access to Electoral Records, either in England or in Scotland. I have used the 192.com live search with some success, but have never actually found a site that gives Electoral info for the period I am interested in.
Thanks everyone for your information!