There are lanyards - and then there are lanyards.
Most European armies of the era up to, and including early WWII, differentiated between other ranks, as well as Non-Commissioned and Commissioned Officers, though the American Army didn't.
Then - there are the 'lanyards' that are merely 'ropes' of one construction or another - usually varnished or waxed - sometimes fitted with a sliding knot.
Ours were varnished and fitted with sliding knots and snap links, while Europeans seem to've merely looped through the loop.
The purpose was to retain the weapon in the event of running out of ammunition during a Cavalry attack, or when the saber was warranted during same - but 'that' didn't happen all that often.
The purpose of the floorplate lanyard loops on the Model 1911's magazines was to retain the magazine after it had run dry - and there are photos extant of pre-WWI Cavalry Troopers with several lanyards looped across their chests - and attached to both the weapon and to spares.
It was a short-lived issue, since tactics changed dramatically, though lanyards are still issued in the U.S. Army - notably for MP's.
If you're thinking of re-creating an Imperial Russian Impression - then look to publications done by 'Osprey's Men At Arms' series, since I seem to remember something dealing with that.
On the other hand - if you merely have a Number 3 Russian and are using it in context with the American frontier era - there's no need.
Vaya,
Scouts Out!