You cannot connect a Lightning connector to a USB-C port. The two interfaces are not directly inter-workable without use of a suitable interface converter.
Your iPad generally cannot supply sufficient power to an externally connected USB storage device. iPad is only able to supply adequate power to very low power devices - which for the most part, Flash and SSD based storage devices require more power than the limited supply from the iPad can support.
As such, you must provide an alternative source of power.
For USB-C equipped iPad, if the storage device does not have its own source of power, the simplest and most effective method is to connect both you iPad and USB storage to a powered USB Hub. The hub then supplies power and connectivity between the iPad and connected USB accessories.
You must also ensure that your storage device is correctly formatted as FAT, FAT32, exFAT - or if used exclusively with a Mac computer, APFS is also supported. iPad also requires external storage devices to have only a single data partition. Most small capacity devices, such a the ubiquitous “thumb drive” (a.k.a. Memory Stick) are factory formatted to FAT32.
I hope this explanation and guidance is helpful in resolving any difficulties.