RWS chamber oil is non-petroleum oil (silicone based).
If you're going to use something else, use a silicone based oil.
Why? Well, we don't know what the seal(s) used in your airgun are made from and using a non-silicone based lubricant could be detrimental to them. The Lyman case lube you show in your picture is petroleum based, so don't use it.
Likely any number of other silicone lubricating oils will work. Spot On treadmill lubricant costs $15 for a 4 ounce bottle, for example. Super Lube food grade silicone oil runs about $7 for a 4 ounce bottle. Both available on Amazon.
A 1/2 ounce bottle will run you a long time, because you only need to apply a drop on the tip of the CO2 cartridge, where the seal will mate up to it. A 4 ounce bottle will last you MUCH longer.