Is it easy to take subway from bao'an airport to Lao Jie station on Chinese New Year eve (7 Feb)?

Both taxi and subway are good choices for you, and they are available on New Year eve.
If by taxi, the cab fare is around CNY120 in the day time.
If by subway, there won't have so many people. And yes, you need to take the airport shuttle to get to Hourui Station. Then take the direct subway Luobao Line. Besides, subway won't be closed during Chinese New Year. But most shopping malls and markets will be closed from New Year's Eve to Jan.3 of the Lunar New Year.

Thanks Emily for the useful info . One more question from me, since most of the shops closed on eve and first 2 days of Chinese New Year then any idea where normally tourists go for a reunion dinner on Chinese New Year eve in downtown ? Thanks

As I know, most large restaurants and shopping malls in downtown area will operate normally. You may easily find a restaurant for a reunion during the festival. Good luck!