No, you do not bind off and pick up stitches separately.
Keep all of your live stitches from the garment on the left hand needle. Then when you knit the edging inwards from the outside edge, you join the last stitch of the edging to the next live stitch on the left hand needle - knit 2 together through back of loops.
Just remember, you are knitting the edging at right angles to the garment.
When I attach lace edging in this way I usually slip the first stitch on the return row. The pattern does not say to do this, but if you find it doesn't lie flat, try slip 1.