Well...the damage may already have been done.
Any system relying on a recovery/backup mechasim...may also rely upon a hidden partition which the system manufacturer created...to effect the restore. If that partition was deleted or damaged by you when you shrunk your Windows partition...any backup/restore mechanism may not work. You would have to review the details of the Lenovo system to see.
FWIW: You could just as easily created a new primary partition on your system. The major difference between the two types is that you cannot boot Windows from a logical partition...bootable partitions are primary partitions and a hard drive can have up to 4 of those. I don't mean to imply that all primary partitions are bootable (because they are not), but they have the capability of being made bootable and, therefore, suitable for installing Windows.
When a user creates logical partitions...they are subdivisions of the extended partition which is creazted . To differentiate the primary from the extedned...diskmgmt will use a different color for the two. I haven't used logical partitions in years so I may be all wrong about these things.
I believe that...because a logical drive/partition...is part of an Extended Partition (by definition)...that you cannot remove the primary partition without first removing the Extended partition. The "extended partition"
To answer your question....an extended partition can exist without a primary partition. The extended partition can then be broken down into logical drives/partitions. It's not necessary to have a boot/system partition on that hard drive.
I'd say that you need to take a look in Disk Managment...and see just what the structure of your hard drive looks like.
And...any restore-to-factory-defaults...should be exactly that. Same hard drive, same partition size, same files as at initial purchase of system. IMO, using that mechanism will result in deletion of the data storage area you created.