Can I open source my project under Apache 2 if it uses a LGPL3 library without modifying it? I'm not planning to distribute the LGPL3 library along with the code.
I would be OK with this. This is a common pattern. My Apache-licensed code can depend on an unmodified LGPL-licensed library when it dynamically links with it.
My understanding is that LGPL3 allows this type of use,
I would be OK with this too. My LGPL3-licensed code can depend on an Apache-licensed library. In this case, my Apache-licensed code may be subject to the LGPL3 terms in general.
but I'm not sure if Apache 2 allows this, on the other hand since no other open source code is actually distributed with this project, can Apache 2 prevent merely linking/referencing against LGPL3 library?
As I said above, I am able to link to an LGPL3-licensed library from my Apache-licensed code that can stay Apache-licensed.