Handled properly, an LP can endure hundreds and hundreds of playings with no noticeable degradation, so I don't think it matters on which playing you decide to record it. I certainly don't think an LP becomes "accustomed" to a stylus and if it does, it suggests the LP was damaged somehow in playback.
What I do think is critical is that the LP be scrupulously clean. Even a new LP should be cleaned before playing.
What I do think is critical is that the LP be scrupulously clean. Even a new LP should be cleaned before playing.