Find a way to get some training in the new skills you need for the new role, and you'll stop spending a lot of time and energy in figuring out what it is you need to do.
When I made the same shift from senior developer to lead, I also found that the work had changed. In my case, I already knew that would happen, and was looking forward to the challenge of developing new skills, so motivation was not a problem for me. Your challenges now are less technical and far more interpersonal. I resisted that promotion for years, until I finally came to appreciate the truth in "People are the most interesting puzzle you'll never solve."
In my experience, changing your perspective on an issue can remove the lack of motivation. In your question you several times comment on having to work harder, but that's not really true. Your work is different, and you need to learn new skills to be effective at it. The learning new skills and the friction of not doing them effectively is what looks hard at the moment. Assuming you learn the skills, in a year or two you'll wonder what was so difficult.
I found a set of podcasts that have been terrific for teaching me the skills I needed: Manager Tools, home at http://www.manager-tools.com. There's a "basics" feed, which is the place to start - with hundreds of podcasts available in the full feed, it can be overwhelming without a little guidance.
Manager Tools gives me a lot of tools to use in attempting to solve the people puzzle, and keep track of what they're doing along the way. Using those tools simplified how I approached the new tasks that were part of a team lead job, and reduced the stress of not knowing how to do the new tasks effectively. Having someone tell me "do it like this, it works" broke me out of a lot of points where I was spinning in place (feeling like I was working harder) just because I didn't have the skills I needed yet.