It depends on what you need, but I'd say yes, as long as they natively support whatever language and database you're using. I usually use Lighttpd for specific (non-general) projects requiring lighter implementations. Actually, I think that the more specific your requirement is you may switch to more tailored solutions. One examples are WAF's like Rails or Play!, they use non-LAMP components like SQLite, Ruby or Java in addition to using their own webservers.
I hear that nginx is good for static pages, but every article is silent about, what is the actual difference between apache and nginx when dynamic, heavy websites are involved.
If your problem is one of performance, specially if it's related to dynamic content, I think nginx is a very good option in terms of flexibility, lighthttpd performs better than Apache in some cases but if your requirements are specific you may need some configuration with ngnix and a high-performace server like FastCGI or Starman.
perhaps you don't know but this is part of a common problem for large implementations, it's usually known as the c10k problem, you may want searching that term to find more detailed information
