You don't have to prepare lesser restoration
The Alchemical Mastery feature is granting you a separate way to cast lesser restoration. It is independent of the Alchemist spellcasting feature.
It is similar to, and may well be explained by comparison with, Warlocks' Mystic Arcanum.
Choose one 6th-level spell from the warlock spell list as this arcanum.
You can cast your arcanum spell once without expending a spell slot. You must finish a long rest before you can do so again.
Note that the Warlock does not learn the spell from this feature, and that there is no way for a Warlock to learn 6th level warlock spells using their spellcasting feature. The feature grants a way to cast the spell without knowing (ie. having learned/prepared) the spell.
If Alchemical Mastery was intended to require lesser restoration to be prepared, it could (and probably should) be phrased differently, for instance along the lines of Wizards' Spell Mastery:
Choose a 1st-level wizard spell and a 2nd-level wizard spell that are in your spellbook. You can cast those spells at their lowest level without expending a spell slot when you have them prepared.