I am looking for a conceptual treatment of Lie theory and Noether theorems that uses tensors calculus rather than exterior calculus.
I know that tensor calculus is not optimal for these subjects, particularly since much of Lie theory does not assume a metric and covariant derivatives are secondary, but I am not a professional mathematician and I find tensor notation much easier to read. Whenever I read differential geometry using modern notation I seem to spend most of my energy just parsing formulas.
I would also prefer a more geometrical than algebraic treatment.
I am not 100% sure it would match your expectations but have a look at Peter Olver's Applications of Lie Groups to Differential Equations.
Specifically for the mathematics surrounding the Noether theorem you also may wish to look at the book by Yvette Kosmann-Schwarzbach, The Noether theorems. Invariance and conservation laws in the twentieth century, Springer, New York, 2011.
As for the Lie theory per se, Naive Lie theory by John Stillwell could be helpful.