Fix two data lists intertwined

ClearAll[unTangle]
unTangle = Module[{l = #}, 
    l[[All, All, 2]] = Transpose[Sort /@ Transpose[l[[All, All, 2]]]];l] &;

Examples:

Row[{ListLinePlot[{l1, l2}, ImageSize -> Medium], 
  ListLinePlot[unTangle @ {l1, l2}, ImageSize -> Medium]}, Spacer[10]]

SeedRandom[1]
lsts = MapIndexed[{#2[[1]], #} &] /@ RandomReal[1, {5, 50}];

Row[{ListLinePlot[lsts, ImageSize -> Medium], 
  ListLinePlot[unTangle @ lsts, ImageSize -> Medium]}, Spacer[10]]

Alternatively,

ClearAll[unIntertwine]
unIntertwine = TemporalData[Transpose[Sort /@ Transpose[#[[All, All, 2]]]], 
  {#[[1, All, 1]]}] &;

Normal[unIntertwine@{l1, l2}] == unTangle @ {l1, l2}

True

Normal[unIntertwine @ lsts] == unTangle @ lsts 

True

ListLinePlot[{l1, l2}]

l0 = Transpose@{l1[[All, 2]], l2[[All, 2]]};
ListLinePlot[{Max /@ l0, Min /@ l0}, DataRange -> {0, 13}]