I play Morde a decent amount and I'd be lying if I said I was the most experienced person with him.
However; I've only lost 1 lane ever (vs Jarvan 4) and my other losses have been due to teams raging at each other and surrendering even though I was in the midst of bringing us back in those games.
Runes: Mpen reds, hp scaling yellows, flat ap blues, 2x flat ap quints and a ms quint
Build: start boots/ pots, try to get giants belt first b if not get an amp tome. First build rylais, sorc boots, then hextech revolver.
From there you have a lot of options, same with your leveling scheme. Always level your e first, and get your ult as possible. Need tankiness? get your w. Need dmg? get your q. Same with your build need tankiness? Get items like abyssal scepter, spirit visage, wardens mail, zhonyas. Need more damage? get items like: rabbadons, death fire grasp, liandry's torment. That combination of liandry's and rylais is devastating to their hp bar especially when you have ignite and your ult.
You should basically be unstoppable. Spam your e as much as possible to keep your shield up and harass even the people who supposedly counter you.
I got counter picked by a malzahar earlier (supposedly one of morde's toughest matchups) and I absolutely ground and pounded him.