11 Interacting with foreign code
One of Rust's aims, as a system programming language, is to interoperate well with C code.[/quote]The Lua VM is a C API, so yes, you should be able to use it from Rust easily.

My question is how much logistic and scripting support should I get if I write a game engine in rust....[/quote]Can you re-phrase the question? I don't understand what you're asking.

Can anyone probably guess if a systems programming language will be used in future to write game engines, and not managed application languages?[/quote]That's been the trend so far, with C++ being the popular systems programming language. It will be a long time until managed languages replace C++ for this job.

I started using rust because everybody says that C++ is less used now, and its future is just like cobol.

A System programming language is usually used to mean "a language for system programming": that is, a language designed for writing system software as distinct from application software.[/quote]

The very names of these categories should be a hint -- "systems programming" languages are well suited for low level "systems programming" tasks, where you're thinking about bits and bytes and structures made up of them.
"Managed" languages are not as suitable for these tasks, because they've already done a lot of the systems programming tasks for you (e.g. they've implemented a GC for you, often precluding your own implementation). Instead, these languages are often called "productivity languages" (because programmers are supposedly more productive when using them) and are designed to make "application programming" easier, where you're thinking about abstract objects and high-level "business logic", instead of bits and bytes.

Systems programming languages are great for writing game engines, but aren't the best for writing games. Higher level ("managed"/"application"/domain-specific) languages are generally able to implement high-level game logic with less code, and with less effort from the programmer, but make low-level operations harder or even impossible to write.

For example, Lua is often used for game programming, but it is of little use to engine programmers, because it's lacking in the fundamental data types required by a lot of low-level systems code (e.g. it can't manipulate bytes or raw integers).
C# (+ .NET) is a great "managed" language, and it lets programmers write code very quickly, but when used for systems programming tasks, it becomes complicated and extremely verbose (arguably more verbose than C++).

The standard practice in the games industry is (IMHO):
*Engine runtimes and performance-critical systems are written in C/C++.
*Game logic is written in a "productivity language", such as Lua or C#. Sometimes C++ is used here, but only when the game team are more comfortable/experienced with it than other languages.