The lyre-shaped lucet is technically out of period (though prettier and easier to use). Instead, early lucets were generally a simple tube with prongs at the top ends (most finds being a hollowed, carved bone).
They can also make elliptical cross-section braid using the "twisted-stitch:" method that's pretty good for couching cord - as long as it's made with a fine fibre.
Braids can be made with multiple colours - either interchanging on individual stitches or groups of stitches, or used as a gimp thread for decorative purpose. Beads can also be added either in straight rows or looping around the braid in a helix pattern.
Braids made on a lucet need to be made from thread that can take a bit of abrasion, as the technique will cause the thread to rub against the horns of the lucet when the loop is pulled tight.
Instructions (including how to make 2 colour and beaded cords) are available at this page: http://www.stringpage.com/old/lucet.html
Another excellent resource is the Lacis book: "Lucet Braiding: Variations on a Renaissance cord" by Elaine Fuller ISBN 18911656066
You can get a lucet from: http://merchants-medieval.com/cockerel/