Children with ADHD can be prone to depression, since much of the feedback or attention they get is negative -- either criticism for not focusing or trying hard enough, or a stressed parent pointing out that their lack of focus is now making everybody late.
My son is younger, but has similar low motivation and poor self-esteem, as well as an ADHD diagnosis. Keeping in mind that ADHD is really a cluster of symptoms and what works for one boy might not work for another, here are some strategies that could help.
Concentrate on positive statements and praise. Children who have ADHD get used to feedback about how bad they are at paying attention. If they can't meet expectations, they internalize the message that they're just flawed, bad children -- whereas the reality is they just need to put in more or different effort than other kids. This can lead to a lot of self-blame and low self-esteem, and also to giving up easily. Trying a lot of activities might even lead to lower confidence and less commitment to practicing. This is yet another activity I'm bad at. Why should I even bother practicing to try to get better?
Look for opportunities to praise even the littlest successes. Most importantly, make praise about the effort applied, not about the child. Reducing the amount of criticism (even what we thought of as gentle and constructive) and instead praising good behavior has helped our son reduce his level of self-disgust. Especially for a child who's struggling with motivation and can't find a reason to put in effort, tying your praise to him showing motivation and effort can be helpful. Even just "Thanks for setting the table when I asked," or "I'm so pleased that you sat down and did your homework straight through, what a good effort" -- the way my son's face just lights up at these moments honestly makes me feel terrible that he seems to be craving praise so much.
Watch closely for whatever it is that does capture his interest. This doesn't need to be an organized activity (e.g. sports) or even necessarily a productive one (e.g. computer programming). It can be a favorite TV show or comic book or set of toys.
My son can talk almost endlessly about the characters and plot twists in Ninjago (a LEGO line of toys with an associated cartoon show), and we've generally encouraged this. It leads to parent-child LEGO building sessions, some interesting conversations about snakes (the bad guys are the Serpentines), and discussions about whether the bad guys are really inherently bad (some of them have switched sides, etc.). I have absolutely no idea how this might ever be turned into a life's calling, but rather than really worry about that now, we're just supporting his passionate interest in something.
Be willing to remind gently and repeatedly that something needs to happen. There are few things more annoying than being in a rush in the morning and going to your son's room expecting him to be dressed and ready, and instead finding him sitting on the floor in underpants and one sock reading a comic book. I used to have a what the hell are you doing, we need to leave and you're nearly naked, we're going to be so late because of you response. I'm still working on transitioning to checking up on his progress repeatedly, and instead saying Just wanted to remind you to get dressed, the second time taking the comic book and simply saying I want to help you focus, I'll take this to the kitchen so you can grab it on your way to the car. He is capable of getting dressed quickly, just needs occasional reminders to stay on task and help removing distractions from the area if they're really overwhelming.
Have well-defined responsibilities. Structure's important for any child, but moreso for those who struggle with attention and memory. Regardless, they are simply things that need to be done. We don't really tie basic chores (feed pets, set table) into any reward or punishment structure unless we notice a significant deviation from expectation, and we prefer sort of surprise rewards... "I noticed that you took care of the dog every day this week without me reminding you. That's really awesome effort on your part, and I'm sure Spot appreciates the attention too. Want to go pick something out at the bookstore?"
I think the conversation about CBT would be best had directly with his child psychologist. (It's not impossible, but she should have a more professional and informed opinion about it than me.) Bring your specific concerns about motivation and long-term depression up with her. To some extent your son should get to control the emotions he wants to discuss (or hide) in their sessions, but she can also help guide the conversation. Ideally, helping her understand his behavior will make the visits more productive and purposeful.
Finally, read all sorts of resources for ADHD children -- the Internet is full of ideas and suggestions, and as I mentioned what works for one child may backfire for another. The NIMH has Tips to Help Kids Stay Organized and Follow Directions. Another Answer (the Question was about a younger child, but still potentially helpful) I gave has a list of resources at the end. In general, I've found tips for helping ADHD children to be useful even for non-ADHD children.