Assume that you need to build a linear model to make predictions for new observations, and that there is uncertainty about which subset of variables should be included in the model. You are only interested in making predictions, there is no theory available to guide variable selection, and you aren't interested in drawing causal inferences.

In this scenario, when wouldn't you use LASSO? Everything I read makes it sound like the perfect tool in this situation. However, when I have a nice new hammer in my hand, all problems look like nails, so I would like some examples of reasonable scenarios where variable selection and avoiding overfit are important, but when LASSO is either entirely inappropriate, or unlikely to be the best option. There are other threads on why you should use LASSO; I want to know why I shouldn't.