No, you can't. When you miss the first flight, they will cancel your second flight and you will not fly that day.
The reason is because of the way airlines sell airfares. They competitively price market by market. For instance, NYC-Lahore is a fairly competitive city-pair, and they price lower to win your business away from, say, Emirates. Washington DC to Lahore is not as competitive and they have a more direct flight, so they can command higher prices. I am not saying prices are like this, but as a hypothetical example:
Lahore via Doha and Washington to NYC: Emirates $2000, Qatar $1900
Lahore via Doha to Washington: Emirates not offered, Qatar $2500
The smart consumer figured out to book to NYC instead of DC, then get off at DC and never take the DC-NYC hop... And save $600. Thre are websites to help you find deals like this. This is called "Hidden City ticketing". The airlines consider it a scam, and do everything possible to shut it down.
They can't do anything about the example I just gave. But in the other direction, you bet they can shut it down, and they do! If you don't board in NYC, they assume you are trying the hidden city "scam" and cancel the entire rest of your itinerary, including any return trip. And they use the same rules for all flights, even ones where "hidden city" gives no advantage.
So you must call them and get their consent to change your itinerary. This may (or may not) involve a repricing.