Tamper evidence
Updated
Separating the legal question from the commercial one, because they have different answers here.
What is actually required
Ordinary cosmetics are not subject to a general tamper-evident packaging requirement the way certain OTC drug products are.
So for a cosmetic lip balm this is a choice. If the product is on the drug side, check the requirements that attach to it rather than assuming the cosmetic answer carries over.
What buyers require
A different matter entirely. Plenty of retailers and most distributors will not take an unsealed personal-care product, and they will not negotiate about it.
It is worth asking before you print packaging, because adding a seal later can mean a different cap, a different band size or a carton.
The options
A shrink band over the cap and neck. The standard answer, cheap, and it needs a heat source.
A shrink sleeve over the whole tube, which is also your label. More expensive, better looking, and it removes the label adhesion problem entirely.
A carton, which gives tamper evidence, a large printable surface and somewhere to put a Drug Facts panel that will not fit on the tube.
That last one is worth a thought on the drug side, because it solves two problems at once.
Where it matters most
A lip product goes on the mouth. Customers are more sensitive about that than about a hand cream, and a market stall is exactly where they are most sensitive.
The cost per unit is small. The judgment it earns from a first-time buyer is not.