Should it be permitted if I bought the book, and I use the scan when the physical book isn’t nearby?

Definitely.

Rabbi, even if this is permitted according to Jewish law, shouldn’t it still be prohibited on moral grounds?

Definitely.

On that same topic, is it permissible to lend a book to a friend? If so, how is that different from our case here?

This really requires further clarification. Good question. But this question exists even without assuming, as I do, that there is a prohibition of theft here. Even according to the halakhic decisors who hold that this is encroachment or a violation of a ban and the like, what is the difference between lending and copying? I think the difference is that when you copy, you take an additional copy for yourself, and that is theft. When you borrow and read, that is just additional use of that same copy, and that should not be prohibited. And even if you copy, read, and destroy it, at the moment you copied it, you still committed theft.

I wanted to suggest that when a book is sold in some medium (a physical copy or a digital one), the seller permits the buyer to use it only in the standard way for that medium. Meaning, if the seller sold a physical book, he does not permit digital use unless you also buy the digital book, and vice versa. As for lending a book, that is part of the accepted permissions of use for a physical copy.

This reminds me of the story of the American corporation Monsanto (which was recently acquired by Bayer), which developed genetically engineered crops like corn and soybeans and patented them. It sold farmers seeds of the improved crop under a use license that forbade the farmers from using seeds that would grow in the next crop cycle after their initial harvest. In other words, every time they wanted to sow, they had to buy seeds from Monsanto again (even though they already had Monsanto seeds there in their field—just that the license didn’t permit them to use them). More than that: if some Monsanto seeds blew over in the wind and reached a neighboring field and grew there, the neighboring field’s owner was forbidden to make any use of the seeds or the crop. Monsanto also made sure to enforce its license restrictions through a fleet of detectives and investigators, and anyone who violated Monsanto’s terms of use was sued by them with another fleet of lawyers, and it was hard for the ordinary farmer to defend himself against this. You can see some of this in the film Food Inc. or in this YouTube clip: