For LVM and VXVM, I'd add new PVs, and do a PVmove to move all the data to new NetApp hosted PVs, then evacuate the VNX hosted ones out.
In general my suggestion is to migrate as close to the app as possible - ESX Storage VMotion, Exchange DAG, etc, then OS level, if transparent is possible - as with LVM and VXVM, and then finally do cut-overs at the storage level.
VMware is easy if you have storage vmotion. Let VMware do the work for you.
Luns are straightforward going to cDOT using Foreign Lun Import (FLI). The cDOT cluster is inserted between the SAN host and the old storage during a brief cutover event, after which the LUNs are brought onlline and clients continue while Data ONTAP imports the luns. There are details to be considered but that would be my first stop.
For NFS data we have XCP https://xcp.netapp.com to bring 3rd party NFSv3 data into cDOT. Its really fast and its free. It doesn't do CIFS at this point, but there are other options ranging from commercial to robocopy depending on your scale and budget.
If this post resolved your issue, help others by selecting ACCEPT AS SOLUTION or adding a KUDO.
XCP can be used to migrate to 7-mode, it is a fantastic tool, 25 TIMES FASTER than rsync!
Data Dynamics StorageX is another great GUI driven tool that supports both NFS and SMB migrations from 3rd party to NetApp storage.
Regarding SAN migrations, check out this video which shows an Oracle environment migrated to ONTAP9 using Foreign LUN Import. Foreign LUN Import is an ONTAP feature that is built into the OS. Supported starting 8.3. Highly recommended use of 22 minutes: