Since it is only for decoding
This is irrelevant
Is it ok to use this library with closed source software (I guess LGPL allows it)?
LGPL and GPL don't forbid any usage, so clearly yes. Those licenses impose restrictions for the distribution of software, not for their usage,
Is there any codec licensing issue (x264 and x265 are disabled)?
You should check if you are using some of the optional parts of ffmepg which are under GPL. Check the licensing docs which comes with ffmpeg, it contains a list of those parts. Don't expect others to do this for you, only you know precisely which parts of ffmpeg you are using.
Can I distribute the binaries with my application or at worst provide a link to let the user download them?
You can distribute the unmodified binaries of a library under LGPL together with your application without the need to put the latter under LGPL or make your product Open Source. You need to do this in a form, however, that a user can always replace the LGPL lib by another version if they like to. Check and follow the exact license terms which are coming with ffmpeg.
For GPL stuff, you have to be more careful, but if you distribute a software which has the optional feature of using GPL modules which you don't distribute by yourself, but let the user of your application download and install by himself, you are usually safe (but beware, IANAL).
And I picked a release with the following name: win64-lgpl-shared
From the name, I would expect that is what you are after - a version without the GPL parts, as a shared library (which might be exchanged later). But you should either check by yourself that this package contains what this name pretends, or ask in an ffmpeg forum.