I believe any technical leader has a responsibility to review all the code that goes into a codebase.* I am certainly not the only person to feel this way (Joe Duffy as MSFT and Aras PranckeviÄius as Unity have said the same).
Furthermore, I don’t believe the responsibility to review code ends at a certain level. Everyone from an Engineering Manager to the CTO should be reviewing code as well. In my experience, I’m able to do thorough reviews for 5 to 8 people, and more cursory reviews for another 15 to 20.
Code review above a team lead level** is not about micro-management. A manager should never, ever be saying “we do not use lambdas here, use a named function instead.” Instead, try “do you think this would be more readable with a named function instead of a lambda?” Or maybe you say nothing, and observe what happens, and inspect what other code looks like. If lambdas are common in the codebase, either your opinions need more information, or you have done a poor job educating.
Code reviews by managers should be about getting enough information to manage and lead effectively.*** It keeps you up to speed about what is going on, not just in terms of tasks, but in terms of culture. Are people writing spaghetti? Are bad choices challenged? Are hacks put in? Is code documented? Are standard libraries being used? Are the other technical leads reviewing and leading their teams effectively? You can learn an incredible amount through code review, and you need this information to do your job of leadership and management effectively.
*: I believe all programming managers and leaders must be able to program. I find it shameful this needs to be said.
**: It should go without saying, but team leads should be reviewing every checkin on that team.