The first thing to notice is that we don't ask God not to tempt us, but not to lead us into temptation. Sometimes God will allow us to be tempted, for our good or that of someone watching.
The second thing we should be aware of is that there is a difference between temptation and testing. The Lord will not tempt you, but he will test you, as he does all his children. That sounds like a fine distinction, and it feels that way sometimes. I can only tell you my way of looking at it; if it helps, you're welcome to it and if not, you're welcome to throw it away.
God tests us to see us succeed and grow stronger. Satan tempts us so we'll fail and grow weaker,
Simplistic, maybe, but it's worked for me.