1. 可以认为状语从句省略了 I am。即：

So when comparing myself with my classmates, I feel very lucky to live with such a good dad.

= So when I am comparing myself with my classmates, I feel very lucky to live with such a good dad.

2. 也可以认为状语从句的谓语是由一般现在时简化来的。如：

So when comparing myself with my classmates, I feel very lucky to live with such a good dad.

=So when I compare myself with my classmates, I feel very lucky to live with such a good dad.