There are a few things you need to get more involved in to make a move like this, which you can do as a Development Manager (as you'll see from my name here I've been doing something similar myself).
- Project Management - You need to get involved in the managing of projects, this will give you knowledge and experience. Agile things like Scrum Master are OK, but it can help to be doing actual PM tasks. You'll learn about budgeting, planning, negotiation, dealing with third parties
- People Management - You need to learn about managing people, both in terms of work tasks, and career management.
- Higher level technical skills - This is less about things like coding, but more about being involved in technical programs, making recommendations on software/systems purchases, long term planning tech wise (the 10000/20000 ft stuff).
I saw these things as required skills when I worked for a large bank and noticed everyone who moved up was a PM and line manager.
Now how do you make this step? As a lead you can get involved in mentoring, move to line managing a person or two, also get involved in recruitment and interviewing. Also see if you can get them let you to manage a small project, start with a small change/enhancement (maybe a couple of weeks) and learn the ropes. For the tech, look for any relevant programs in your company and volunteer, even for a small role initially.
You can then start looking to move to a dev manager role, some places have people who do a coding/management split so you can do it as a transition.
From there you move up, in my own journey I've gone in a relatively short time from being a lead on a team of five, to managing software development for the company (15 devs/testers/ba), managing projects up to about 12 months in length. My manager is the IT Director and his manager is the Chief Executive, so I can see where the path goes.
It can help to learn your chops in a big organisation, then move into a medium one when you want to move up, fewer levels above you, but more credible experience than being in a small company (the number of Technical Directors I've met from sub ten person companies who are two years out of college).