They clearly ask for the following
Condition for Use: This software is freely available, but we expect that all publications describing work using this software , or all commercial products using it, quote at least one of the references given below.
here https://users.iems.northwestern.edu/%7Enocedal/lbfgsb.html
This would indicate to me that it is not sufficient to cite LBFGSB.jl and thus mentioning their work indirectly or Optimization.jl that may wrap it for example.