Let's imagine I'm making MortPlayer, a video player for iOS which uses a version of the VLC libraries which are licensed under LGPL 2.1 (since that's what you're focusing on). Let's say I want MortPlayer to be closed source.

In other words, VLC owns the libraries, and I want to license them under the LGPL 2.1.

The LGPL 2.1 says:

6. As an exception to the Sections above, you may also combine or link a "work that
uses the Library" with the Library to produce a work containing portions of the
Library, and distribute that work under terms of your choice, provided that the
terms permit modification of the work for the customer's own use and reverse
engineering for debugging such modifications.

Okay, so I must distribute MortPlayer under terms which permit modification and reverse engineering. I can do that. Maybe Apple's terms conflict, but let's assume that's not an issue, let's read on.

You must give prominent notice with each copy of the work that the Library is used
in it and that the Library and its use are covered by this License. You must supply
a copy of this License. If the work during execution displays copyright notices, you
must include the copyright notice for the Library among them, as well as a reference
directing the user to the copy of this License.

Okay, no problem.

Also, you must do one of these things:

Oh boy.

a) Accompany the work with the complete corresponding machine-readable source code
for the Library including whatever changes were used in the work (which must be
distributed under Sections 1 and 2 above); and, if the work is an executable linked
with the Library, with the complete machine-readable "work that uses the Library",
as object code and/or source code, so that the user can modify the Library and then
relink to produce a modified executable containing the modified Library. (It is
understood that the user who changes the contents of definitions files in the
Library will not necessarily be able to recompile the application to use the
modified definitions.)

Okay. I can accompany the work (MortPlayer) with the source code for VLC's libraries, no problem. MortPlayer is executed and linked with VLC's libraries, so I need to 'accompany the work with ... the complete machine-readable "work that uses the Library", as object code and/or source code, so that the user can modify the Library and then relink to produce a modified executable containing the modified Library".

I think that's doable with app stores? I can certainly distribute a zip file with the object files for MortPlayer so that the user can link them against their own version of VLC. The user wouldn't be able to then run the recompiled application, on their device, but that's not specified in the terms...

Honestly I'm a bit surprised, I fully expected to find that this section a) included wording which requires the user to be able to run the resulting linked application, which Apple forbids (asterisk), and then go through b) and conclude that iOS doesn't have a "suitable shared library mechanism" due to its restrictions etc. But I'm instead forced to conclude that you're probably right, at least by the letter of the license.

I read the corresponding parts of LGPL 3 as well, and I can't find anything which requires the re-linked application to be immediately executable on the user's machine there either.

I think my conclusion is that LGPL, both 2.1 and 3.0, is fully compatible with app stores so long as you distribute your application as object code which can be linked against the LGPL licensed libraries? I would be very interested to hear from someone with opposing views about why I may be wrong. I, as they say, ANAL.