I do not have experience with Delphi, therefore my answer may be wrong.
In order to handle your Delphi (or other programming environment) code from LabVIEW, you need the external application to act as an activeX server. Thus, you need to find out if it's possible to do it in Delphi. Unfortunately, I could find just this link related to
activex server in Delphi.
An alternative is to create activeX controls and embed them in LV front panels (comparing with activex server, this solution brings some limitations).
Also, you may consider to have your Delphi application as DLLs (if possible) or executable (controlling it by sending keys and mouse events via windows API)
Hope this helps somehow