Could you post the specs of the computer or make and model?
Need to know if it is A legacy bios computer or a UEFI bios?
This info will tell us if you are using the best version of Puppy Linux for your computer.
Most Puppy versions offer several programs for doing installs.
You do not say which one you used.
You need to boot with the USB live install so you can use the programs in it. Best if you have a F96-CE USB you can boot from.
Because you had Lubuntu installed and it's installer just did everything for you and setup the internal drive the way it wanted to.
Sorry, but Puppy software always provides you choices on what to do.
This how to install is what I would do, if all you want on the internal drive is Puppy Linux. (UEFI bios computer)
viewtopic.php?t=5275
The only difference depending on having a Legacy bios or UEFI bios.
Legacy bios will like it better, when setting up the drive, and making the partition table, you select msdos for type, not GPT.
But all other steps are the same.
WARNING:
Make sure when selecting the drive to work on with Gparted.
You are selecting the internal drive not the USB drive.
Internal drive is most likely going to be sda.
Anytime you give info about what specific Puppy version.
Give the full complete name of the Puppy versions ISO file.
There are several versions of a specific named Puppy and that can make a difference in how stuff works.