Both models are true depending on how you frame the mechanisms of catalysis. As mentioned by @Blues, proteins are highly dynamic. In that manner, a protein will adopt both the unbound active state shown in the induced fit model and the complementary shape shown in the lock and key model.
(apologies since this is the only figure that I could find to explain this concept). Using the above description the induced fit model (E) will change its structure to the E*S model. In the lock and key model, the E state will be equivalent to the E*S state. According to the below figure, this would imply that the E*S state always exists but as it is a few kcals higher in free energy, the state is rarely seen. Thermodynamically, this means that the "lock" always exists but it is an unstable configuration. When the substrate is added to the system, it will stablize the lock and thermodynamically favor an E*S state.
Long story short, the induced fit model is a good explanation of how enzymes morph into an active state but depending on how you frame the mechanism, you are always seeing a lock-key model (at least according to my enzymology professor). Unfortunately, the majority of biochemistry textbook continue to teach using the induced fit model since it is a much easier concept to understand given the majority of undergrads; and 1st year graduates' understanding of statistical thermodynamics.
The induced fit model is more appropriately used to understand the mechanisms of substrate specificity. As hinted by your professor, enzymes will perform their function in the lock-key mechanism. This is true for many serine proteases which all do the exact same reaction. However, substrate specificity can be incorporated by unstabilizing the E*S complex which largely has to do with the E state.