ZeroMQ is safe for use in close-source applications. The LGPL share-alike terms do not apply to applications built on top of ZeroMQ.
You do not need a commercial license. The LGPL applies to ZeroMQ's own source code, not your applications. Many commercial applications use ZeroMQ.
Currently
libzmq
is in the process of relicensing. In the meantime their library is still released with theLGPL
license with a static linking exception.To quote the zeromq website: