Up to about .30-30, maybe a little beyond, you can get away with not holding the fore-end on a lever gun, at least for load development. As mentioned above, my support hand usually ends up squeezing a rear bag when I'm working with a .30-30, the .307, or the .44 Mag 1894 from a bench.
So long as the rest is padded in some way, that is. If not, it may cause damage when the rifle comes back down after recoil. I've seen many barrel band style Marlins shear or break the rear barrel band screw (and crack a few stocks) by smashing down on a hard rest when shot from a bench or an unpadded tripod. (Like the H-style and T-style rests commonly made from steel, 2x4 lumber, and/or concrete, and available at many ranges.)
But the bigger boomers require more control. The aforementioned .444 Marlin is not something you shoot one-handed. Even when rested, a good grip on the fore-end is required. Which, for me, means my hand is rested, not the rifle.
Whether there is a hand on the fore-end, or not, one must be careful to preload the same - as tangolima mentioned.
I have most of my Marlins set up so that the barrel takes all pressure that is put on the fore-stock. The magazine is essentially "free floated" through the stock and only contacts the barrel at the end of the tube (whether barrel band or tenon style attachment). That partial isolation seems to help settle lever guns down by reducing the number of points where barrel movement during firing is forced to interact with the mag tube. But, it also means that preload by a hand, or on a rest, has more influence on the barrel.
A Sub-MOA rifle off the bench isn't a sub-moa rifle in the field, unless I can shoot it that well, in the field.
That is the primary reason why I started shooting NRL22, with a close second being getting my son a lot of trigger time in situations that somewhat simulate hasty field positions (plus stress, score, a timer, and safety considerations in play)
Terrible shooting positions on unstable and awkward props make the shooter find a way to "build" a stable shooting position with their body (and some large support bags, for some shooters). And then you complicate it with tiny, difficult targets.
Standard competition shooting positions, on level ground, are rarely used in the field - at least in my part of the country.
NRL22 will show your weaknesses in a startlingly amplified manner. It is a beautiful thing.
We're not shooting centerfire, and it is not a perfect analog for actual hunting situations. But .22 LR keeps it cheap enough to be affordable, makes it even more challenging (in my opinion), and any awkward precision shooting on reactive targets is better practice for the field than trying to translate from lazy, easy shooting from a bench or prone on level ground.
Some people argue that NRL22 (or NRL-Hunter) is no longer representing "proper" field shots, because off-hand shooting is no longer built into the stages. But I don't care and it doesn't matter to me. I have only made three standing shots on big game in my life. And they were close enough to be repeatable any day, with pretty much any rifle and many handguns - 90 yards (deer), 75 yards (elk), and 25 yards (elk). (Edit: I remembered a fourth. I stopped an antelope with a heart shot, that was mortally wounded by another hunter, but running full speed. ~120 yards, crossing right to left.)
The rest of the time, I found a way to get as stable as possible to make a "perfect" shot, from trees, logs, or other features of the terrain. I don't take shots on big game when I don't have 98%+ confidence in a guaranteed one-shot kill.
I take great pride in being known for the shots that I passed on, as much as the ones that I did take; as well as being known for generally coming home with one round fired per animal tagged. I want it "perfect" - quick, clean, and exactly as I intended.
Sorry about that going long.
If NRL22 discussion is to continue, we can peel it off into its own thread.