Congratulations on Lucy! 
Tethering her to you with the leash is so that you can keep her right with you, in your sight, that way you don't lose track of her, allowing her to sneak off and pee/poop. It can be very handy.
Crating is another way to contain her.
I would recommend a combination of crating,tethering, and allowing her to roam free withing your direct line of sight. Crating is a great way to teach her to become independent. And, you can give her a chew toy, perhaps a kong stuffed with peanut butter and frozen to keep her busy in the crate.
Tethering is really usable for any of the times you've mentioned, sitting at the table, relaxing, or just puttering around. Although if you were just watching a movie, you could have him cuddle with you ! I always love cuddle time!
Tethering her to you with the leash is so that you can keep her right with you, in your sight, that way you don't lose track of her, allowing her to sneak off and pee/poop. It can be very handy.
Crating is another way to contain her.
I would recommend a combination of crating,tethering, and allowing her to roam free withing your direct line of sight. Crating is a great way to teach her to become independent. And, you can give her a chew toy, perhaps a kong stuffed with peanut butter and frozen to keep her busy in the crate.
Tethering is really usable for any of the times you've mentioned, sitting at the table, relaxing, or just puttering around. Although if you were just watching a movie, you could have him cuddle with you ! I always love cuddle time!