Is there a way to access built-in methods source?

Short answer: No.

Long answer: Sort of, but no.

Lua functions are compiled into byte-code when the script first executes. That means the original source is lost. We can see how Lua compiled a particular function using string.dump. Note that you can't usually print it because it will include NULL characters.

function hello()
    local s = "hello"
    for i = 1, #s do
        print(s:sub(1, i))
    end
end

print(string.dump(hello))

If you do a little work to hide the bad characters, you'll get this:

LuaQ   =Workspace.Script   

  A@ ? Á@ `@?E ?Á@ B @ ? \A _ þ ?   hello  ð? print  sub 
                s    (for index)    (for limit)    (for step)    i   

It begins with Lua, then the version number -- Q is ASCII character 51(hex), meaning this is Lua 5.1 code.

Then it gives the location of the script, Workspace.Script. (If you compile with your laptop's Lua it would look like @C:\Users\Blu\Desktop\blah.lua)

There's a bunch of characters strewn throughout that the output doesn't differentiate, but are of course important to Lua.

So, you can sort of get a picture of what happened in hello based on this dump.

Problem: Lua is an embedded language. It's designed to interface with another, lower level language. In ROBLOX's case, this is C++.

Most "built in functions" are implemented in C or C++. This includes the table, string, etc libraries, as well as all of the ROBLOX functions, methods, etc.

If you try to string.dump them, you'll just get the error

unable to dump given function