Show me the tutorial where I can build, _in C_ a bare bones working (tail recursion) implementation of the lambda calculus with type inference and dependent (algebraic?) types
Type inference and dependent types don't go well together (already System F doesn't have type-inference), although it depends on the details of what you mean by dependent types.
Tail recursion is a concept of compilation and does not show up in an interpreter.
Note also that C has higher-order functions (via function pointers). The only relevant difference from lambda-calculus is that C functions must be named, cannot be nested and must exist at compile time. But conceptually these restrictions make little difference to the understanding of what lambda does: it creates a function.
Finally writing something like that (to the extent that the requirements make sense) is gonna be really painful in C. If you understand the lambda-calculus well enough to know what dependent types are, the implementation language should not make much of a difference.
I think the easiest way to learn the lambda-calculus program in a functional language. The second easiest way is to read the theory, after all the lambda-calculus as a calculus is incredibly simple, and you can hand-wave away the problems of bound-variable renaming. A slow-paced textbook like Hankin's "An Introduction to Lambda Calculi for Computer Scientists", and doing the exercises in the first few chapters should do the job.