If you want to help him resolve his issues, you're going to have to become involved in them. Time, listening to him, never breaking his trust - no matter your good intentions - and taking that 3am phone call of dispair and offering hope.
If you cannot do this, do not try. Does it really mean that much to you? Or is it an inconvenience to your "now"?
Suggest a sabatical and let him figure it out in his own time.
It can give him time to figure out things by himself and also the absence of work could be a big motivator, that is, we engineers often find intrinsic motivation in building, designing and solving problems. Maybe giving him some time to miss that joy could rekindle it.
It's good that you are looking for options and trying to understand.
That means you are not dealing with someone who cannot get motivated. That's the good news.
The bad news is that there is likely one or more things that have demotivated him. A big part of a team lead's job is to remove friction that may grind down your devs. If I were you I'd try to remove demotivators, because with them there you are going to have a much harder time motivating him.
A big thing you can do to remove the demotivators is to find the friction, and remove it. Easier said than done as there are many sources of friction: bureaucracy, health concerns, meetings, busywork, bad skill to role fit, toxic co-workers, and more. But if you can find and eliminate any of these, that will help.
Another thing to consider is that if you have one demotivated person with visible signs, you may have other people feeling demotivated who just aren't to the visible stage yet. If it sounds like I am talking about demotivation as a contagious meme, it's because I've found that to be the case in the past.
Do you do monthly or quarterly one-on-ones with each of your team? Do a one-on-one with them, find out how they are feeling, their goals and aspirations, their pain points. Make it clear the one-on-ones are off the record, and honor that. I've found it sometimes helps to do a SWOT (Strengths, Weaknesses, Opportunities, Threats/Risks) chart for each team member and use then when planning work efforts.
Once you have removed the demotivators you have now brought him back up to around zero motivational drift, but he is still not motivated. This where incentives like work from home, more independent project work, conferences, flextime, team building etc. come into play. If possible, encourage people to work outside - sunlight helps with mood and health in many ways. If he has financial issues, without going into specifics o individuals, see if you can persuade your company to offer the benefit of a wellness plan that includes both physical and mental therapy. In the long run this will be an amazing benefit for your company.
Use the material from the one-on-one with him to determine which incentives to use. Remember to offer these incentives to the team as a whole. Also remember that all behavior, given sufficient context, is rational from some point of view - there are reasons behind his behavior.
If all of the above does not work, it may be time to counsel him out. I am not talking about firing, but about sitting him down, explaining that it seems like he is not a good fit for his role or company, and asking if he will let you help him find a new job with another (noncompeting) company. If he is amenable, have HR help him look for a job and find something that motivates him. This process itself will give you valuable info on what demotivated him in the first place, that you can use to prevent further attrition.