modern cell counters should all be able to communicate with LIMS systems. At our lab we have a XT2000, and it is connected to a LIMS called Swisslab.
However, I would always ask both companies involved (i.e., the company of the cell counter AND that of the LIMS) in what way those systems could communicate. Normally, both companies should present descriptions of the interfaces and required data format.
When introducing such connections, it is always helpful to have experts of both companies at hand. You will probably not figure out the mistakes if your connection and data transfer does not function properly, unless you are a computing expert yourself.