I chose Go for the Turing Machines because I enjoy writing it, and planned to blindly use Go again for the Lambda Calculus for the reason above, but if you have a recommendation I'd love to hear it!
Although I never wrote a Turing Machine interpreter in the lambda calculus, I did write one for its close cousin, the Brainfuck language [2].
[1] https://www.irif.fr/~krivine/articles/lazymach.pdf
[2] https://gist.github.com/tromp/86b3184f852f65bfb814e3ab0987d8...