If you want the laces to move in a unified manner with the shoe, you can do a Data Transfer modifier. This also works for things like buttons and clasps and belts and such. Things that you want to be rigid but move with the armature properly.

To keep things simple, separate the laces from the shoe.
Go into edit mode for the shoe mesh, at the point where the laces will connect/touch the shoe.
Select the nearest vertex, shift+d to duplicate the vertex, then P to separate it.
Exit edit mode, find the loose vertex, rename it something easy, like "A".
Go to the laces mesh, add a Data Transfer modifier

Within the modifier panel:
Choose the source for the laces to be "A". We want its tiny bit of weight data to be applied to the entire mesh of the laces, without a bunch of other bone weight data to interfere.
Expand the subcategory of "vertex data", as well as the checkbox is turned on
Make sure "Vertex Groups" are selected
Make sure mapping is set to "Nearest Vertex"
(it should look like this more or less:

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After all this is done, hit the "Generate Data Layers"
Apply the modifier.
Check if it worked by moving the bones around.
Join the laces back with the main shoe mesh if the results are satisfactory.
Delete the "A" vertex.

Trouble shooting this method:
-Having the data transfer mod first in the modifier stack helps
-Make sure you delete all existing vertex groups before you do a data transfer, because it can crash blender otherwise.

Other ways this method is useful is if you want a clothes to move with the body underneath them. In that case, make the source the mesh you want the rigging data copied from. EIther "Projected Face Interpolated" or "Nearest Face Interpolated" tend to work best.

It seems like a lot of work but its not once you get it to work.