There are numerous natural oils, fats, nut butters and waxes that can be used for this purpose such as shea butter and olive oil.

What people used at any particular time and place would vary according to what was available and what the latest fashion was. The key wax/fat/nut-butter/oil ingredient (often a combination of these) could be coloured and perfumed with other ingredients such as lavender oil, peppermint oil, beetroot juice, carmine (etc.)

Home made lip-balms and other cosmetics are still widely used today by people who can't or don't wish to buy off-the-shelf products. If you search google for 'natural' lip balms you will find plenty of recipes to try (please ensure you check whether you are sensitive or allergic to any ingredients before doing this.)

These will often have short comings compared to purpose-designed cosmetics such as not being as long-lasting in their effect or not being as convenient to apply, but many of the commercially available products are simply adaptations of these recipes.

An exception is the widespread use of petroleum jelly in modern products which is a synthetic material rather than being naturally occurring. That did not occur in cosmetic products until the mid 19th c.

Here's some reading on

Victorian Cosmetics

and

Ancient Egyptian Cosmetics

I've chosen these two widely spaced apart, in both temporal and geographic terms, examples to illustrate the longevity and universality of the basic recipes. For example the ancient Egyptians were using beeswax for lip balm and thousands of years later the Victorians were still doing the same.