Dustin Johnson is making a strong run at the 153rd Open Championship, and his performance at Royal Portrush has caught attention. After three rounds, Johnson sits tied for 22nd at 4-under par, giving him a chance to climb higher on Sunday.Johnson started his week with a 2-over 73 on Thursday, a round that included three birdies, three bogeys, and a double bogey. On Friday, he bounced back with a solid 2-under 69, carding five birdies against three bogeys. Moving day was his best showing yet as he shot a bogey-free 67, 4-under par, to climb up the leaderboard.His form didn’t go unnoticed by LIV Golf, which shared an update on X while Round 3 was still ongoing:"@DJohnsonPGA shoots an impressive bogey-free 67 (-4) He currently sits T15 #TheOpen @4AcesGC_."Former LIV Golf CEO Greg Norman’s son, Greg Norman Jr., also responded to the post and wrote:"A top10 finish tomorrow and its an exemption to next year's Open"However, by the time Round 3 concluded, Johnson had dropped to T22 on the leaderboard.Here is Dustin Johnson’s hole-by-hole scorecard from Saturday’s round:Out (Front 9): 34 (-2)Hole 1 (Par 4): 3 – BirdieHole 2 (Par 5): 5 – ParHole 3 (Par 3): 3 – ParHole 4 (Par 4): 4 – ParHole 5 (Par 4): 4 – ParHole 6 (Par 3): 2 – BirdieHole 7 (Par 5): 5 – ParHole 8 (Par 4): 4 – ParHole 9 (Par 4): 4 – ParIn (Back 9): 33 (-2)Hole 10 (Par 4): 4 – ParHole 11 (Par 4): 4 – ParHole 12 (Par 5): 4 – BirdieHole 13 (Par 3): 3 – ParHole 14 (Par 4): 4 – ParHole 15 (Par 4): 4 – ParHole 16 (Par 3): 3 – ParHole 17 (Par 4): 3 – BirdieHole 18 (Par 4): 4 – ParTotal: 67 (-4)Is Dustin Johnson playing at The Open Championship for the last time?Dustin Johnson’s future appearances in Major championships could be uncertain after this season. While his 2020 Masters victory gives him a lifetime exemption at Augusta National, qualifying for the other three majors might get harder.Johnson required a special exemption to compete in this year’s PGA Championship at Quail Hollow, and his 10-year exemption for winning the 2016 U.S. Open at Oakmont will expire after next year. This means he will likely need to qualify for both the U.S. Open and The Open Championship moving forward.Although the R&A and USGA introduced pathways earlier this year for LIV Golf players to qualify, Johnson admitted he isn’t sure about taking that route."But you never know. I mean, if it works out in the schedule, and I’m not in the Open, I want to play here, and I want to be here playing," Dustin Johnson said via Golf Magic."So I would definitely think about it. But if I play well and I play how I should, I'll be in the Open next year."This season, Dustin Johnson has played in all four Majors. He missed the cut in the first three, finishing 3-over at The Masters, 12-over at the PGA Championship, and 10-over at the U.S. Open. His career-best finish at The Open remains a tie for second in 2011.