Get net then or don't play shite bags with no net.
My internet is plenty fast.
*queue bragging image opportunity for fun*
Its not that simple though. Both parties can have 100Mb/s down and up and still get horrible lag. Most of it is due to poor netcoding by TN and how the game itself handles lag. The other half just comes down to the route your connection makes to the other player. The less hops the better, but isp providers don't always take the shortest hop. You can tunnel your connection to make shorter hops, but given the nature of p2p that isn't very simple.
Example, you could play someone down the street, get a ton of lag, yet play someone in a different state and get little lag. If your packets decide to go up the east coast and take 30 hops, it doesn't matter if the guys right next door, its going to slow down waiting for your packets to make its route. A proper netcode can alleviate some of that, but sadly DoA5 does not have such a thing.