Mr. Poe - lactose intolerant or not?

[Foxy]

In TWW, Mr. Poe takes the Baudelaires to meet Captain Sham at the Anxious Clown so he can go through adoption paperwork with Captain Sham.  When Mr. Poe orders his coffee, he specifically asks for nondairy creamer.  However, a few pages later, Captain Sham orders Cheer Up Cheeseburgers for everyone at the table.  So my question is, is Mr. Poe lactose intolerant or not?  He didn't order the cheeseburgers, but he didn't object to eating one, either.  Also, he may have suggested  the Cheer Up Cheeseburger to Eleanora in TUA; I cannot quite remember.  But if he is not lactose intolerant, why order nondairy creamer?

If Mr. Poe were lactose intolerant, then his coughing might somewhat be explained.  People with lactose intolerance are more likely to have inflammation of the gut, leaky gut, etc., which would make Mr. Poe more susceptible to catching colds and having a cough.

[Grace]

most people are, so, yeah, likely. but he does recommend the cheer up cheeseburgers..... hmmmmm.

[Hermes]

I would have thought he ordered non-dairy creamer because of the possible fattening effects of cream. (he could just have taken milk, of course, but this may not have occurred to him.)

[Dante]

Accepting the premise that Mr. Poe might be lactose-intolerant, perhaps he's also inattentive as to which foods might contain lactose and which don't; that strikes me as plausible.