This stage technically Texas and Cincinnati are still possibilities for the #3 pick. The lowest possible the Sox can fall as of today is 8th.
Texas has 90 losses and 6 games to play, so if they lose all six, and the Sox win their last six, Texas would pass them. The Sox own the tiebreaker, so we only need 1 Texas win or White Sox loss to eliminate the Rangers.
Cincy has 91 losses with 5 games left to play, so they can also get to 96 losses. The Sox own the tiebreaker here as well, so again they only need one loss or one Cincy win to eliminate them.
San Diego has 94 losses, and 5 games left, so they can get to 99 losses as well. The Sox won the tiebreaker so would pick first in the event of a tie, meaning the Sox actually need 4 losses or Padres wins to eliminate them.
Detroit has 93 losses and 6 games left so they can get to 99 losses. The Tigers are the one team left that the Sox do NOT have the tiebreaker with, so to eliminate them the Sox need a combination of 5 Tigers wins and/or 5 Sox losses.
Miami has 94 losses and 6 games remaining, so they can get to 100 losses. If the Marlins play on the last day of the season, the Sox would need a combination of 5 losses and/or 5 Marlins win to eliminate them. Where it gets interesting is if the Marlins don't make up the last game, the Sox would actually need to finish with more losses. If the Marlins lose out, and finish at 61-100, the Sox would still need to lose all six games to eliminate them.