Woods is not the only big name to struggle in the blustery conditions on Scotland's west coast as Rory McIlroy will begin his second round at seven over and likely needing an under par round to make the weekend.
Lowry had been usurped at the top of the leaderboard late on Thursday by unheralded Englishman Daniel Brown, who posted a six under 65.
However, the Irishman, who won his sole major at the British Open in 2019, picked up birdies on the first, fifth and eighth to make the turn with a two-shot lead.
Brown, the world number 272, remains Lowry's closest challenger but dropped back to five under after five.
Woods was adamant earlier in the week that he is not considering retirement and feels physically better than 12 months ago.
But the 15-time major champion cut a sorry figure as he trudged around the Troon links, dropping three shots on the front nine to slide to 11 over par for the tournament.
With the projected cut at four over, Woods, 48, seems certain to fail to complete four rounds for the sixth time in eight majors since a car accident in 2021 left him with severe leg injuries.
Strong winds ensured low scoring remained difficult with the sixth, which had been the longest hole in British Open history on Thursday at 623 yards, reduced by 20 yards due to the conditions.
World number three Xander Schauffele recovered from a difficult start to make the turn at two under.
The recently crowned USPGA Championship winner had dropped back to even par before back-to-back biridies at the seventh and eighth.
World number one Scottie Scheffler is also lurking at one under after a level par front nine.
Attention later turns to McIlroy's attempt to recover from a disastrous opening round of 78.
The Northern Irishman's chances of ending a decade-long drought to win a major already appear gone.
But the world number two has only failed to make the cut once in his last 14 majors.
US Open champion Bryson DeChambeau also has work to do to hang around for the weekend as he begins his second round at five over.
Two-time major winner Justin Thomas is well poised to make a push for the final group on Saturday as he starts at three under.
