Australia's Lee, whose two majors include a Women's Open at Pine Needles two years ago, made consecutive bogeys at the turn and then played mistake-free the rest of the way for a one-under 69 at Lancaster Country Club.
Saso, the Women's Open champion at Olympic Club in 2021, steadied herself from a rocky start by playing bogey-free over her last 12 holes to salvage a 71.
They were one-under 139 with half of the 156-player field taking on a Lancaster course that wasn't getting any easier in the afternoon.
Still to be determined was whether that score would hold up at the end of the second round. But it already was clear the weekend would not include Lexi Thompson in what likely is her last US Women's Open. She had four straight bogeys around the turn and shot 75 to finish at 13-over 153.
Also packing up early was Rose Zhang, who was making a run toward giving herself a chance until missing too many par putts. She shot 72 and was 11 over par.
Most telling was Saso being asked to describe her best shot and Lee asked about the one shot she would like to have back. Both had to turn toward a scoring terminal showing their scorecards, needing to jog their memories about the rounds they had just completed.
That's the kind of golf a Women's Open, particularly on a traditional course like Lancaster, can generate. It's about grinding, getting to the next hole and not doing anything to ruin a round.
Saso opened with a 68 for the 18-hole lead and got into trouble early, coming up short of the green at No. 11 that sent the ball rolling back down the fairway, and then hitting into the back bunker on the par-three 12th hole that caused so many problems in the opening round.
"It's a bit difficult to stay calm compared to normal events," Saso said.
She managed just fine, making a trio of key par saves until she removed stress from her game over the final hour.
Lee was playing in the group ahead and got going on the 12th hole. The pin was back and to the left for the second round - it had been in the front on Thursday, when Nelly Korda made 10 and 52 balls went into the water.
She hit to 3 feet for birdie, then rolled in a 20-footer on the next hole. She got back under par with a 12-foot birdie putt struck with confidence on No. 5. Otherwise, it was all pars on her second nine, and she was fine with that.
"I love playing US Opens. I love the challenge. I love the difficulty," Lee said. "I just love that I really need to think about what I'm doing and be strategic."
Asterisk Talley, the 15-year-old who was on the winning US Women's Amateur Four-ball Championship team earlier this month, had 15 pars in her round of 71 and was part of the group at one-over 141 from the early starters.
