Hello Julia,
to do this, you need to use the custom provisioning procedure. this will replace the cloning function of LVM. Please take a detailed look at the customization blog i created.SAP Landscape Virtualization Management (LVM) Overview of Customization Options
basically you have to create your script, use it in a provider definition and use this provider definition as one of the custom prov. steps. then you need to enable your system fro custom prov. in the settings of the source system. Also keep in mind that you can only refresh a system after you have done an successful initial copy
You should involve SAP consulting int his project, since it is not easy to achieve this on your own.
Kind Regards
Michael