Great to see your motivation and strategic approach in aiming for a career in consulting from an engineering background. Diversifying your options is a smart way to increase your chances of landing an offer, and I applaud your thoroughness.
While MBB (McKinsey, Bain, BCG) are indeed the most prestigious consulting firms, there are many other excellent firms out there. You've mentioned LEK, Oliver Wyman, Kearney, and EY, which are all fantastic options. In addition to these, here are a few more to consider:
Strategy& (PwC): A part of the PwC network, Strategy& offers a combination of strategy consulting and professional services, giving you a wide range of experience.
Accenture: Known for their strong focus on technology and digital transformation, Accenture is a leading consulting firm with a broad range of services and industries.
Deloitte: With their Strategy and Operations division, Deloitte Consulting offers a mix of strategy and implementation work across various industries.
Roland Berger: Especially strong in Europe, Roland Berger is a global player that offers interesting opportunities.
AT Kearney: A global management consulting firm focusing on strategic and operational CEO-agenda issues.
ZS Associates: Particularly if you're interested in the life sciences or health sector, ZS has an excellent reputation.
FTI Consulting: Known for their work in corporate finance and restructuring.
Booz Allen Hamilton: Particularly known for their consulting work with the U.S. government.
Don't forget boutiques and industry-specific consulting firms, too. Depending on your areas of interest, some of these might be a perfect fit.
Finally, remember that while the firm's reputation is important, it's equally crucial to find a firm whose culture and working style align with your own. Try to connect with current or former employees of these firms to gain insider perspectives.
Good luck on your journey into consulting! If you have further questions or need help preparing for your interviews, don't hesitate to reach out. I specialize in helping candidates like you transition into consulting and would be happy to support you.