I've walked all these and the Pennine Way both ways. Walking North to South or vise versa made little difference, it's all about when, where and how much rain you have. The UK weather is variable any time of year, that's what makes hiking here interesting.
I loved walking Lejog but make sure you've done some long distance walking before starting it and you travel light weight, under 10kg base weight if camping. I found that you can plan a really good route but when you get walking it's best to be flexible with the route, to allow for the weather and how your body is on any particular day. I don't like walking on hard surfaces but during Lejog, when it rained I often was happiest on the cycle ways and roads instead of boggy fields. Covering easy mileage and getting closer to my destination was more satisfying than a nice path.
I walked the Pennine Way with a dog (Collie cross Whippet), it was tiered by the end of the day and completed the walk but many peoples dogs don't apparently.