Reason Non linear Lineweaver–Burk plot
The linearity of a Lineweaver–Burk plot assumes that your system follows standard Michaelis–Menton kinetics.

Not every enzyme system follows Michaelis–Menton kinetics with all the assumptions made in its derivation. There are a number of reasons for non-linear behavior, including cooperativity, substrate inhibition, substrate activation, limiting cofactors, isoenzymes, and non-steady-state kinetics. 

Further reasons for a non-linear plot involve experimental issues. Depending on your experimental setup, you may not have accurately measured the initial rates of some of the faster conditions, which can lead to non-linearity of your Lineweaver–Burk plot. If you're operating under conditions which may lead to product inhibition, you might also see non-linear behavior.