Lapthorne, a 28-year-old from Middlesex, and Alcott beat David Wagner and Koji Sugeno 6-2 7-6 (4) to become the All England Club's first ever champions in this discipline.
Celebrations between the pair cannot go on long, however, as they meet in the singles final on Saturday.
"It means absolutely everything, it was a great match," Lapthorne said on court during the presentation ceremony.
"When I dreamt as a kid playing here it was like this, full.
"It means the world to me, it means absolutely everything, I have been to the Paralympics, I have been to other grand slams, but this means everything.
"I am thankful to the All England Club for giving me the wild card.
"Tomorrow we go up against each other and I hope that everyone comes out and supports us."