Wilson has scored four goals since joining the Evo-Stik Southern League side at the end of last month and the 19-year-old striker is set to stay with the Poppies until January 2.
Boothroyd told the Cobblers' official website: "Lewis got a couple more goals for Kettering on Tuesday night and I'm really pleased with how his loan is going there.
"I spoke to Lewis on Monday and he was a rather depressed figure after their 7-0 defeat at the weekend but as I said to him, I've been there before and the important thing is that you bounce back quickly as a player and as a club.
"The point of Lewis going to Kettering was for him to score some goals and build up his match fitness, I don't think he's quite ready to go into our first team just yet but going out on loan and scoring goals will do his confidence the world of good.
"We keep a very close eye on things and I'm sure when he does come back to us he will come back a better player.
"Lewis is a strong character and he loves playing football. He's not played nearly enough football for us and that's why we wanted to give him this opportunity.
"He's there for a little while longer and then we will look at things again in the new year."