It has also been described as "the feature of nature that says experimental results are independent of the orientation or the boost velocity of the laboratory through space".
[1] Lorentz covariance, a related concept, is a property of the underlying spacetime manifold.
Irrelevant Lorentz violating operators may be suppressed by a high cutoff scale, but they typically induce marginal and relevant Lorentz violating operators via radiative corrections.
This is also true for the third class, which is furthermore protected from radiative corrections as one still has an exact (quantum) symmetry.
A detailed summary of the results of these searches is given in the Data Tables for Lorentz and CPT Violation.