First, let's imagine what the situation would be like if your app was open source.
The user cannot modify the app on the store in any way (they cannot change the libraries it uses) but say the app provides a link to the code. Then they can modify the code (change the dependencies for instance), recompile it, republish it as their own app on the store. So, the user is not actually limited to use or distribute a modified version (even if they cannot modify the version that you distribute).
Now, let's come back to your problem. LGPL does not force you to use dynamic linking. You can instead, for instance, provide object files for your software that the user will be able to link (statically) to any version of the library. Thus, suppose that the user wants to build this alternative version. You could make the object files available on the internet; or if you want to sell the app through the store, you could include a written notice that if someone has bought your app, they can request for the object files. The user won't be allowed to republish your app with alternative version of the library on the app store. But at least in the case of Windows apps, there is a developer option that allows you to run these apps without going through the store (mostly for testing). The user could use this mode to run their alternative build of your app and that would not contradict the terms of LGPL in any way.
Note that the same applies to Google Play (a similar developer mode exists) but not to Apple Store (where you have to pay a fee to Apple to use such a mode). Thus, you cannot use a LGPL library in an iPhone app.
EDIT: let me add some more details to convince you that I'm not merely giving an opinion.
Here is the relevant part of the license:
4. Combined Works.
You may convey a Combined Work under terms of your choice that, taken together, effectively do not restrict modification of the portions of the Library contained in the Combined Work and reverse engineering for debugging such modifications, if you also do each of the following:
d) Do one of the following:
0) Convey the Minimal Corresponding Source under the terms of this License, and the Corresponding Application Code in a form suitable for, and under terms that permit, the user to recombine or relink the Application with a modified version of the Linked Version to produce a modified Combined Work, in the manner specified by section 6 of the GNU GPL for conveying Corresponding Source.
1) Use a suitable shared library mechanism for linking with the Library. A suitable mechanism is one that (a) uses at run time a copy of the Library already present on the user's computer system, and (b) will operate properly with a modified version of the Library that is interface-compatible with the Linked Version.
As you can see, I'm not inventing my claim. LGPL is often known as the license which allows dynamic linking but all too often it is thought as the license which forces dynamic linking. This is not correct and an alternative solution is possible (solution (0)).
Additionally, from the GNU FAQ:
Does the LGPL have different requirements for statically vs dynamically linked modules with a covered work? (#LGPLStaticVsDynamic)
For the purpose of complying with the LGPL (any extant version: v2, v2.1 or v3):
(1) If you statically link against an LGPL'd library, you must also provide your application in an object (not necessarily source) format, so that a user has the opportunity to modify the library and relink the application.
(2) If you dynamically link against an LGPL'd library already present on the user's computer, you need not convey the library's source. On the other hand, if you yourself convey the executable LGPL'd library along with your application, whether linked with statically or dynamically, you must also convey the library's sources, in one of the ways for which the LGPL provides.