word choice - Using "lesser" or "smaller" in reference to an abstract quality

In Italian "piccolo" (small) has two comparative forms: "più piccolo" and "minore". While "più piccolo" can be used to refer either to physical size or age difference, "minore" generally refers to age difference or to an abstract quality, rather than physical size.

So, Italians can correctly say:

1. 
   

   Our room is "più piccola" than yours.

   
   


2. 
   

   The incident is of "minore" importance.

   
   

It is clear to me that in "1" case the correct English word to replace "più piccola" is "smaller", but I'm not sure whether in "2" case one should replace "minore" with "smaller" or with "lesser", or if both are correct.

Can anybody explain if there exist a parallelism between Italian and English in the sense above and if "smaller" and "lesser" are both correct in "2" case?