I think the crucial difference is that Lua doesn't have the emphasis on pointers and address-arithmetic that C does. Zero-based array calculations are really useful for that, but for simpler array usage, either style seems to work fine.
So while I still favor zero-based indexing, I think the context matters a lot, and one-based indexing is not always a problem.
It's sort of like driving on the left or on the right. You just get used to one and you think it's the right side :).
What surprised me is that even that didn't actually seem to be a problem in practice [for me], even when frequently switching between zero-based (C++) and one-based (Lua) languages...
Not sure quite what you mean by network building, but IO/networking is libuv-based so should be pretty good. There is TCP client/server functionality built into the language and UDP is coming soon.
As far as web, there is http://juliawebstack.org/.
None of this is polished yet and there is still a decent amount of work to be done on the core language. Additionally, since Julia is targeted for technical computing, the standard library includes linear algebra support and requires BLAS, which is great unless you don't need it and are on a system with memory constraints or want to incorporate Julia into another application, although there has been talk of decoupling the linear algebra support from the rest of the language. But yes, Julia the language should be suitable for all of these purposes.