Occasionally I make offers where there are several lots with the same items.

However, it is possible to get confused and offer on the same lot twice, or on another lot intended for another user.

In "My Offers" it would be informative to include the lot number with each offer, so I can double check them.

Agreed. Or put some type of message like "You have offered on this lot" on lots when you are searching for the items.

I don't do too much trading though so if it already does that, please correct me :)