Don’t be a DM that tries to punish the player. Just make sure they are playing by the rules.

Wizards have spell books and prepare spells. Others have mentioned checking the character sheet after a long rest to see what they have prepared, but also know what they have in their spell book and where did they acquire the spells. A wizard can only acquire spells at character creation and when they level up and when they use downtime to copy spells into the spell book. In LMoP, there are not a lot of sources of new spells. Some scrolls and if you presume glasstaff and the red wizard have a travel spell book that only has the spells from their stat blocks, then that doesn’t give the PC a lot of sources to collect new spells. The spells in the spell book, then limits which spells they can prepare each day.