DIY Syringe Lubricant
There is a product known as plumbers grease, used for faucets and other plumbing applications. The water from those faucets is used for drinking and cooking and other household applications. The grease is also known as PTFE lubricant, also known as teflon compound.

A liquid oil would not have much staying power and may react with the walls of the syringe. Butter would eventually turn rancid as would other organic compounds. 

Teflon is known for lack of reactivity as well as durability under high pressure and temperature, although it's unlikely you'd be dealing with either.

A thin film of teflon/PTFE/plumbing grease would provide a substantial reduction in friction with minimal contamination and also give you good duration of use. You would also want to consider if the hot glue you used is water resistant. Some products of that nature will slowly degrade when exposed to water.

All of the above is my opinion, backed up with some real world use and online research independent of this question.