.... On May 8 my flight with Delta from Seattle to Milan was rescheduled to next day due to circumstances beyond my control. As such I would not be able to make Lufthansa flight the next day.....
Did you change the DL flight or DL change the flight?
With tickets booked with travel agents they "own" the ticket and changes have to made with them. This can be expensive, as often they have hefty fees in addition to the airline fees. But anyway a non refundable non changeable fare (elcheapo) may be not able to be changed at all. Buyer beware.
On line TA's are not really TA's:- just computer programmers. I suspect some of their
customer service people have never flown or maybe even never seen an aircraft close up.
What did your travel insurance have to say?