I have a question about the relationship between Faraday's and Lenz's law from a graph of the emf of Faraday's Law compared to the voltage in a coil. My question is whether or not this graph supports Lenz's law. Also, is it possible to determine from this graph if the direction of the induced current is going in the expected direction when the magnetic field is increasing?
You could say something about Lenz law if you had measured the current too (positive or negative). You should measure EMF and current, then cross-plot it carefully because of the signs involved.
If you only calculated V and measured EMF you can't 'prove' Lenz's law because you've used it implicitly (the minus sign at Faraday's law from Maxwell's equations)