Airline delayed my flight by 2 days, refusing refund and incorrect compensation amount

Looking for some advice or clarification regarding expenses/refunds from airlines… I booked a round trip flight from Detroit to New Delhi on United Airlines site. The trip on the way there all aircraft, boarding passes and correspondence was through Lufthansa airlines. On my last flight landing in New Delhi, they lost my bag for 2 days. It was delivered to me but I incurred some expenses due to not having my bag and missed a connecting flight I had to rebook out of my own pocket. For my return flight, New Delhi to Germany was through Lufthansa airlines, then Germany to Detroit was supposed to be a United Airlines flight. 36 hours before my departure I received an email from Lufthansa notifying me that they had rebooked my flight for 2 days after my originally scheduled flight. I promptly called the airline and tried to get a reason for this and see what my options were. They basically told me if I wanted the soonest available flight closest to my originally booked itinerary I would need to pay an extra $500 to switch back. I was already unsatisfied with them losing my bag, I just didn’t have it in me to give them any more of my money. I am just confused how this is a legal or legitimate business practice, I’ve never had this happen to me before. I ended up just staying on the flight they rebooked me for 2 days after my originally scheduled departure. I saved all of my expenses I incurred for the extra 2 days for food, hotels etc. Once back in the states I submitted all of my expenses and asked for a refund. Per Lufthansa’s website per US D.O.T. I should be entitled to a refund due to significant change in my itinerary, significant change including 6 or more hours later than the scheduled time.

https://www.transportation.gov/individuals/aviation-consumer-protection/refunds https://www.lufthansa.com/us/en/refund

Once back in the states I submitted all of my receipts along with the request for the refund for the return trip. Lufthansa has pretty much only emailed back a copy and paste response saying they only owe me $170 usd. However, I submitted food and hotel expenses that total $421 usd. All I get back is a copy and paste response, I am absolutely sick of dealing with them but I just cannot stand that airlines walk all over their customers like this. Also, I submitted my expenses for my lost luggage (the cost of the connecting flight + had to buy a new dress for a wedding I attended, original dress was in the lost bag. Total expense was around $130 USD). If I’m not mistaken, aren’t airlines supposed to cover this as well? Either way, I never received any email or correspondence regarding the lost luggage expense I submitted. Do I have any legal leg to stand on? Do I get my lawyer involved? Am I filing the expenses incorrectly? I would attach screenshots if I could, I’ll try to answer as many questions as possible in the comments. Any advice/perspective would be appreciated. TIA!

Location: United Stares, Midwest