On a general note - juliac is an experimental development under a beta version of Julia. Windows adds it’s own specific difficulties. Fortunately there are brave people there who are not afraid of all the frustrations to help the community to improve the tools 
. However with all the effort I wouldn’t really expect to it to get production-ready in the close future.
Another solution, which may or may not be acceptable for a use case like yours, would be to instruct the customer to perform a standard Julia installation on their computer, and the let your GUI software execute a Julia script to start a server, talk to the server, and shut it down in the end - all completely transparent.
That’s what I have done with my LVServer.jl + LabVIEW0.jl packages ([ANN] LabVIEW0 - Calling Julia from LabVIEW using ZeroMQ). The communication is over ZeroMQ, the data sent over as json (for large data amounts, sending in binary format was also supported). Unfortunately that all happened to become a solution without a problem, at least for me, but it worked nicely
If there exists a working ZMQ implementation on the Lazarus side: The LVServer.jl can probably be used as is, otherwise easily adapted.
There are also some other packages in the JuliaInterop. See also (may or not be relevant):