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For electromagnetic induction, Lenz's law states that

"the current induced in a circuit due to a change in a magnetic field is directed to oppose the change in flux and to exert a mechanical force which opposes the motion."

When we want to find the direction of this 'mechanical force', we use Fleming's Left Hand Rule and use the direction of our thumb (which indicates the magnetic force). Therefore, can it be said that the force trying to oppose the motion from Lenz's Law is always a magnetic force created by the magnetic field and the induced current?

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Lenz's law actually is a qualitative description of Faraday's law of induction $$\mathcal E=-\frac{\partial \Phi_B}{\partial t}$$ where $\mathcal E$ is the induced EMF due to the changing magnetic flux $\Phi_B$ over time. By definition of EMF, we therefore have $$\oint\mathbf E\cdot\text d\boldsymbol \ell=-\frac{\partial \Phi_B}{\partial t}$$

So really Lenz's law is concerned with non-conservative electric fields (forces) rather than magnetic ones. However, Lenz's law only talks about magnetic fields if you just need to know the direction of the induced EMF, all you need to know is how the magnetic flux in changing. This change in magnetic flux is the opposed. But this opposition is due to induced electric fields.

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