Prestige Monitor
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Marking ball on the apron

As far as I am aware, in relation to the method used to mark a ball that is to be lifted, the Rules make no distinction between whether the ball is on the green or if it has to be marked off the green - e.g because it might assist or interfere with another player, or if preferred lies are in operation.

Rule 20-1 and Note and Decision 20-1/16 Method Used to Mark Position of Ball

FAQ also helpful.

So far as preferrred lies are concerned the R&A has a specimen local rule which says

“A ball lying on a closely-mown area through the green (or specify a more restricted area, e.g. at the 6th hole) may be lifted, without penalty, and cleaned. Before lifting the ball, the player must mark its position. Having lifted the ball, he must place it on a spot within (specify area, e.g. six inches, one club-length, etc.) of and not nearer the hole than where it originally lay, that is not in a hazard and not on a putting green.

A player may place his ball only once, and it is in play when it has been placed (Rule 20-4). If the ball fails to come to rest on the spot on which it is placed, Rule 20-3d applies. If the ball when placed comes to rest on the spot on which it is placed and it subsequently moves, there is no penalty and the ball must be played as it lies, unless the provisions of any other Rule apply.

If the player fails to mark the position of the ball before lifting it or moves the ball in any other manner, such as rolling it with a club, he incurs a penalty of one stroke.

Note: “Closely-mown area” means any area of the course, including paths through the rough, cut to fairway height or less.

*PENALTY FOR BREACH OF LOCAL RULE:
Match play – Loss of hole; Stroke play – Two strokes."