Lehecka beat US Open runner-up Ben Shelton 6-4, 6-4 in Prague as the Czechs bounced back in their second-round qualifying tie following Learner Tien's straight-sets win over Jakub Mensik in the opening singles rubber.
The USA are record 32-time winners of the competition but have not lifted the trophy since 2007.
Christian Harrison and Austin Krajicek are set to take on Czech pair Adam Pavlasek and Patrik Rikl in Saturday's doubles, with Shelton due to play Mensik before Lehecka faces Tien in the reverse singles.
South Korea seized an unassailable 3-1 lead over India in Seoul as Kwon Soon-woo and Chung Hyeon both staged dramatic comebacks in their first singles rubbers on Friday, before the former sealed their spot in the Final 8 with a 6-1, 6-2 victory over Sumit Nagal today.
Kwon recovered to beat 367th-ranked Dhakshineswar Suresh 3-6, 6-3, 6-4. Chung, a former Australian Open semi-finalist whose career has been derailed by injuries, also came from a set down to overcome Nagal, 2-6, 6-4, 7-5.
"I felt a lot more nervous than I have in a long time," Kwon said.
"Of course, I usually feel some nerves, but today they were particularly intense. At the beginning, my vision was almost blurred. From the second set onward, I began to feel more relaxed."
India had cut the deficit in half after winning the doubles rubber, but were unable to mount a comeback.
Austria and Belgium are all locked at 1-1 in Vienna.
Jurij Rodionov beat Gauthier Onclin in straight sets to put Austria ahead, but Zizou Bergs fought back to see off Lukas Neumayer 2-6, 6-4, 6-2.
Host Canada seized a 2-0 lead over France at Quebec City.
Canada's Liam Draxl, ranked 205th in the world, upset France's Arthur Rinderknech 6-2, 7-5, in the opening match and world number five Felix Auger-Aliassime outlasted France's Quentin Halys 7-6(5), 4-6, 6-3 to put the hosts in command.
Three other ties start on Saturday.
Newly-crowned US Open champion Alexander Zverev makes a quick return to action for Germany, who must get past Croatia in Halle in their quest for a first Davis Cup crown since 1993.
Spain continue their tilt at a seventh title against Chile in Santiago, while Britain, featuring surprise Wimbledon semi-finalist Arthur Fery, welcome Ecuador to London.
The seven winners this weekend will join hosts and three-time defending champions Italy in Bologna in November's eight-team Finals.