rionorte,
Depending on the exact nature of the lace structure, you may try the following (some additional steps may be needed):
1) Group the whole lace structure if not already;
2) Copy the Group to the front and hide the copy, then select the original Group;
3) Object>Path>Offset Path by a positive amount sufficient to close all gaps within the lace structure, then hide or delete the original Group;
4) Pathfinder>Unite or Merge, and apply the desired colour(ing);
5) Object>Path>Offset Path by the same amount as in 3) only negative;
6) Show the copy Group hidden in 2).
This should give you a coloured background filling the lace structure in the form of a path. You may wish to adjust the shape of the path where it covers the gaps/openings between the outermost parts of the lace structure.
It corresponds to the somewaht similar suggestion in this thread about a contiguous background behind letters: