I was ordered by coach to "stop" tying laces as, at comps, parents aren't allowed in dressing rooms. So, we had them tie their own. However, I will say that it was a bit of a disaster at first. I'm good at lacing skates; I got "trained" by a coach on how to do it, and have strong fingers and callouses. When my kids took over lacing their own, they ended up with them being too loose on the foot and too tight on the ankle, and there was a fair bit of time spent off the ice as their coach made them relace them to make it correct. Eventually, they did get it, but it took time, and their coach did have to check them regularly to make sure they were done right.
In terms of laces, I found the best ones for my DD were the Jackson ones with the rhinestones on the toes (and the Jackson ones without too, but, they weren't as much fun for the 8 year old she was then.). They held the best, and were the easiest on small fingers.