I have a project consisting of a core library with a number of platform-specific wrapper libraries. I want to release it all under an Open Source license (maybe MIT or LPGL).
I also want to sell the compiled binaries and support on platform-specific stores as an optional convenience to users. They will be able to build it themselves for free if they prefer, directly from the source.
Is this possible with standard licenses? Are there any considerations I should be aware of?
Open source licenses don’t forbid anyone from selling the software for a fee or for providing additional services for a fee.
The main reason that open source software is usually provided for free is that if you ask a fee for the distribution, anyone is allowed to under-bid you and distribute the same software for less money (or even for free).
The difference between the two licenses you mention is that with the LGPL, any modified versions of your software must remain under the LGPL license (with the requirement that source code must be available), while the MIT license allows modified versions to be distributed under a different license (including a closed-source license).
It is possible, but you won’t forbid someone to get the source code, perhaps adapt it, compile it, and distribute the resulting binary.
If you use the LGPL license, the entity redistributing binaries should (AFAIK) publish (as LGPL) the modified source code. If you use MIT license, that entity could redistribute binaries without even publishing its modifications.
I am not a lawyer, so ask your lawyer for details.
Read at least the LGPL license and its FAQ.