Yes, the model with the smallest AICc is judged to be the best model based on the empirical evidence provided by the sample of data. You might also consider prior evidence and theoretical findings if available to temper your decision.

The difference in AICc between the best model and any other model can give you an idea of the support for the other model. If the difference is less than 4, then the other model has substantial support. If the difference is between 4 and 7, then the other model has considerably less support. Finally, if the difference is more than 10, then the other model has essentially no support. The smallest AICc difference in your case is about 300, so based on this evidence alone, the Lognormal model is the best model of those in the comparison.

You can use AICc to compare different kinds of models (e.g., linear model versus neural network model) as along as AICc is meaningful for each model and the criterion was calculated for the same data set.

You could now use the Parametric Survival model through the Fit Model dialog. Select lognormal for the error distribution and add your five-level treatment (Insecticide). I recommend, if possible, that you represent these levels with a continuous variable for more information. The linear predictor can include transformations of Insecticide, such as powers, to address non-linear response. That model will get your LRT going!

Learn it once, use it forever!