No. LEGO's help page on earning and spending points says points can't be shared or transferred, and warns that doing so could lead to account termination. That applies to LEGO Insiders and to old VIP points alike.
What that means
- Points belong to the account that earned them. There is no "send points" option for friends or family.
- Don't pay someone for their points or let anyone else use your account to collect points. LEGO says that can cost you the account, points included.
- Points are also tied to your region. They can only be used on the regional LEGO.com site where the account is registered.
What you can do instead
- Let the other person earn their own. Anyone aged 18 or over can join LEGO Insiders and earn points on their own purchases. Registering sets also earns 20 points per set.
- Gift what you get with your points. If you redeem points for a physical reward, the reward is yours to give away. Rewards are claimed with promo codes that are valid for 60 days and are limited by stock. LEGO's help pages don't say whether a discount code can be passed on, so I wouldn't count on it.
- Gift the sets you buy. Points keep earning on your own purchases even if the set is a present for someone else.