I don't think L.L. Bean is in any airline/Amtrak/hotel malls.
But there is a way to get miles/points for L.L. Bean purchases!
Find one of the malls that has giftcertificates.com as a partner. Buy a
gift certificate for L.L. Bean from them - and earn miles/points for giftcertificates.com and have it delivered by email.
And then use the gift certificate to pay for your purchase(s) from L.L. Bean!
I did this - and earned 200 miles from UA!