#lance rest

Lance rest is the correct term, although lance arrest or lance stop would be a more appropriate translation.

The lance arrest is an innovation that first appeared in the late 14th century. As depicted above, it is a metal hook, usually foldable, which is either bolted directly to the cuirass or attached via a removeable pin and staple system.

Lances designed for use with an arrest would be equipped with a ring affixed just behind the hand.

Dosso Dossi, "St. George," c. 1540, Pinacoteca di Brera

When charging, the lance would be set atop the arrest with this ring against it. Upon impact, the arrest would catch the ring, transfering the force of the blow to the user's body, and preventing the lance from being pushed backwards. This dramatically increased the power a couched lance was capable of delivering.

Paolo Uccello, "The Battle of San Romano" (detail), c. 1435-1460, Galleria deglia Uffizi

The arrest was likely developed to help counter the increasing presence of plate armor. As quality plate became more prevalent, the simple couched lance became less effective, so methods were sought to increase its power.

A really good example of how snatched the waist could be in a cuirass. Fairly modest in chest room, but it's important to note that it is quite rounded and not flat.

L18-76 in Schwäbisch Gmünd, late 15th century

I do!

So, earlier on, couching a lance would mean tucking it up into your armpit so a bit of the shaft stick out behind you like so.

(English, ca. 1230-1240.)

Your arm would be severely bent and your hand somewhat forward from your breast, as can be seen here.

(Spanish, ca. 1200.)

There are depictions that show both the palm turned outward,

(English, ca. 1310-1320.)

and the palm turned inward,

(Bohemia, ca. 1321.)

Which would seem to suggest the lance can be held couched either way.

Eventually (late 14th century,) the arrêt de cuirasse, or lance rest, was invented.

The lance was also modified, and a stop rib was added, which would sit just in front of the lance rest, stopping the lance from moving backwards once it struck a target and transmitting significantly more force to the impact.

This doesn't really change the way the lance is held, but the lance would rest (shockingly) on the lance rest, and provides so much extra power that it's suggested that the Great Bascinet (a Bascinet with plate over the throat rather than the aventail of maille which had come before)