I did a frugal install like you suggested but I must not be doing it quite right.
First I did the normal install on the main Lenovo drive - Repartitioned it again giving part 1 FAT32 bootable, part 2 ext4 with folder for installed puppy. This booted fine like normal.
I then made one patition on the sd card drive as ext4 and installed puppy to it. Then I selected the boot to use part 1 on the main drive. When I rebooted, it tried to go to the sd card partition, but failed to find the drive like before.
When doing an install to the SD card do not do anything on the internal drive.
The install on the SD card is a completely separate drive and keep it that way.
Do not do anything to the internal drive that is already setup with a working boot loader for what is on that drive!
The two drives are completely separate drives and setup for what is on them with a separate boot loader for booting what is on the specific drive.
Each drive has a Puppy frugal install.
A separate boot loader on it to boot that Puppy install.
You do not use the boot loader on one drive to boot what is on the other drive.
The SD card needs to be setup with two partitions.
Maybe this step by step will help yo do it correctly using Frugalpup Installer.
Use Gparted program.
Setup the SD card with 2 partitions.
First one, small 300MB, fat32 format, flagged boot and esp. (location for boot loader files, boot partition)
Rest of drive, whatever other partition(s), but one ext3 or 4 format. (location to put frugal installs)
(this is UEFI standard requirement, and some computers, look for a fat32 partition, for boot loader files)
Run Frugalpup Installer main program.
On the main window are selection buttons.
Select the Puppy button, to do the install.
Go through install process, selecting to install to the ext formatted partition.
Note:
When selecting the partition to install to.
A window pops up, giving option to make a directory, to put the frugal install in.
I make this directory and usually name it, the name of the Puppy version.
Carefully read that windows info.
Press enter, makes the directory, not the OK button.
complete the install.
When it gets back to the main Frugalpup window.
Select the boot button.
Select the location (partition) of the frugal install, on the SD card. (this tells it to look on this partition for Puppy installs to make boot menu entries for)
Select the first small 300MB partition on the SD card, as location to install the boot loader. (may need to scroll the selection window)
Select the boot loader type.
UEFI
mbr ->legacy bios boot
both
For your install put both boot loaders on the SD card.
The UEFI will also install the needed files, to support secure boot enabled in UEFI.
When you first boot on a UEFI computer, with secure boot enabled.
A process will start, to allow you to install the Puppy security key, to the computer.
It will add this Puppy key, to the other ones, loaded on the computer.
When complete the SD card will have at least two partitions.
1st one with a boot loader and all it's needed files setup to boot what is on the SD card.
Another partition with the Puppy frugal install.
When you boot with the SD card selected as the boot device to boot from.
(I am assuming you can select what device to boot from)
It's boot loader starts booting the computer and loading the Puppy files on it.
The internal drive is not used to do anything.
If you did this correctly and the computer will not boot to a working desktop.
OK.
This computer cannot boot from a SD card.