Combining lists of lists with random structure

This matches your output:

Module[{i = 1},
  Map[{#, l2[[i++]]} &, l1, {2}]
]

If you don't need l2 separately you can eliminate the use of Accumulate entirely with:

Module[{t = 0},
  Map[{#, # &[t, t += #]} &, l1, {2}]
]

The inner function # &[t, t += #] is just a way to AddTo t but return the old value of t. Equivalently: First[{t, t += #}].

Also,

l3 = Internal`PartitionRagged[Most@l2, Length /@ l1];
Transpose /@ Transpose[{l1, l3}]

{{{3, 0}, {2, 3}, {4, 5}, {2, 9}},
{{2, 11}, {3, 13}},
{{4, 16}, {3, 20}},
{{{2, 2}, 23}},
{{{3, 3}, {25, 25}}},
{{3, {28, 28}}, {2, {31, 31}}}}

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