Skylab 4
The Skylab 4 crew wore coveralls with beta cloth emblems on board the USS New Orleans after the flight. As no custom patch was created by the crew either, there is effectively no embroidered crew patch for the Skylab 4 mission.
The one picture I could find of the Skylab 4 crew wearing an embroidered patch is S73-36766 (right) showing the crew beside a T-38 at Ellington AFB.
Although the image I have is very low resolution it looks to be the AB Emblem patch on the shoulder of Ed Gibson's flight suit.
Other Embroidered Mission Patches
A-B Emblem patch
The AB Emblem Skylab III patch does not have the hallmark of the Lion Brothers patch. Note that the AB Emblem patch was used by NASA on the certificates of appreciation distributed to employees after the mission.
Lion Brothers patch
The Lion Brothers Skylab III patch has the first initials of crew's surnames "CGP" incorporated into the design of the tree as a hallmark. Note that a rare plastic backed prototype version of this patch exists and a yellow border color variant (likely a pre-production sample) surfaced in 2017.
Cape Kennedy Medals patch
This patch from Cape Kennedy Medals looks similar to the AB Emblem version but has a black inner band in the rainbow.
Hilborn Hamburger patch
This patch from Hilborn Hamburger can be easily identified by the dark blue stitching enclosing the right hand side of the grey circular area behind the human figure.
3" Embroidered Mission Patches
Cape Kennedy Medals 3" souvenir patch
This is the Cape Kennedy Medals 3" souvenir patc.
Footnotes
[1] Examples of Skylab 4 Cape Kennedy Medals patch sales:
eBay item no. 180796441400 sold Jan 20, 2012 at $70.99
eBay item no. 130838381286 sold Jan 27, 2012 at $23.49 [In original CKM packaging]
[2] Examples of Skylab 4 Hilborn Hamburger patch sales:
eBay item no. 200883409866 sold Jan 27, 2012 at $11.61
eBay item no. 140962937998 sold Apr 30, 2013 at $115.49 [with HH Skylab 3 patch, both in HH packaging]
eBay item no. 261439690768 sold Mar 31, 2014 at $99.75 [buy-it-now] [in HH packaging]
eBay item no. 252191643098 sold Dec 24, 2015 at $69.95 [in HH packaging]