If I do a first close and do not raise the full target amount, am I obligated to return the capital to LPs who do not want to commit to a smaller fund?

You are not going to be obligated to return the money to investors and it will not be feasible for you to do so even in the unlikely scenario that an inexperienced LP makes an ask like this. This is because the LP's money gets invested into startups as soon as possible. In other words - think of the fund's bank account as a router of LP money into startups.