Salomon boots have a locking lace system - one set of eyelets have a locking grip bit on them -  so that you only have to pull the laces once to get a tight enough fit on the main part of the foot, and you can then leave them looser on the ankle.  This might make things a bit easier, or you could maybe fit a cinching clip on the laces that would secure them above that point (where it wouldn't need to be really tight).  Good Grips make a bag cinch thing (for sealing plastic bags) that might grip laces (but it doesn't seem particularly easy to use).  Otherwise, outdoor shops sell replacement clips like the ones that tighten the cord at the top of a rucksack, that could be fitted to laces.  

Another idea might be to walk in trail shoes instead of boots - again, Salomon have a sliding tightener on their laces, which I've found works well.  If their shoes fit you, you might give this a try.

My mother had severe arthritis so I can sympathise with your difficulty here.  Best of luck.  E

when I was a lad ... we used to use a cord lock, if that's the right term - the little squeeze lock things that you close ruck sack lids with. So you tie your laces permanently with a granny knot or whatever, so that they're loose - cut off the end and fit the cord lock. (but not in that order)

To tighten them you pull the whole lace with one hand as you say, and lock with the plastic doobry whatsit.

There's another product here, but never seen it in action, or 1000mile, the sock people do one here which looks a bit like my method above called lock laces - you can get them on amazon.

i have an idea but may not be what you thought of!

Look here, this was recommended to me at a time I was having difficulty but I don't actually need them...yet