The most obvious derivation of this old man icon to me is from earlier Nordic fertility images, e.g. the 'Frey' figure from Rallinge, the 'Thor' image from Eyrarland.  Graham-Campbell (2013, 166-7) described this beard stroking as a sign of virility.  G-C also illustrates a small wooden figure from Gnezdevo that may fall within this group although the beard appears to be lost.  The Eyrarland figure was probably made in a Christian context so that we cannot rule out your example as being a late survival of this artistic tradition.  It would, however, be interesting to know whether this figure was actually carved for the church or has been reused.  A second possibility, given that the 'heretical' Stedinger are often described as a Frisian people is whether or not such pagan survivals were common in the Low Countries.  It would not be unreasonable for some of the Old Testament patriarchs to have acquired elements of pre-Christian fertility figures.  Although the closest example I can think of from Christian iconography is St Luke from the late 6th century Corpus Christi College, MS 286, f.129v.

Regarding the lion, does your church have any connection, now or historically, to St Mark who is frequently depicted in association with a lion.

in Dutch there is a saying pulling your beard and it means trying to avoid punishment or chores by faking illness.

In the chanson de Roland verse 2414 and there Charlemagne does to show his misfortune

the dictionnaire du moyen français:

Tirer la barbe de qqn. "Se montrer d'une familiarité excessive" : Si Dieu ne t'a voulu pugnir pour les grans pechez que faisois, Et s'il t'a laissé d'impugnir, il ne s'ensuit pourtant que doiz Tirer sa barbe de tes doiz Par ta folle oultrecuydance (RIVIÈRE, Nef folz D., 1497, 550).

Lode a similar concept to the French usage is also used in English with the tugging on a beard a symbol of dominance over a rival, I seem to recall that Robin Hood does it in a few legends and also I think Hollywood used it in the Errol Flynn version.  A variant on this is probably the language used to describe the damage Drake did to the Spanish fleet at Cadiz, he 'singed the King of Spain's beard'.  Both these usages and the French are probably descended from the pagan Germanic association of beards and virility, something vividly illustrated in Njal's saga where lack of a beard was used as a taunt and this was regarded as sufficiently offensive to justify killing the taunter.  The beard as a symbol of virility means that to pull a man's beard is virtually the same as groping his genitals.  Interestingly the Rallinge figure is simultaneously stroking his beard and masturbating, also interesting is that the Rallinge figure and this church carving have very similar hand positions leading me to wonder whether or not the church figure is copied from a pagan original that was indeed performing both actions.

There is also a practical aspect to this in that in combat grabbing a man's beard can give one the advantage by enabling one to pull an opponent off balance.  In this case I do not think that this is relevant to this figure since it clearly depicts a man tugging on his own beard ala the old 'fertility' images.

However, your comment on the Dutch usage makes me wonder whether there is a Biblical version where tearing at the beard is a sign of grief/powerlessness, unfortunately I do not have any versions to hand except for the King James which I would not trust to render such details accurately.  It might be interesting if something with access to a good Hebrew or Greek version could confirm this since this might allow for an interpretation of this figure as either humility or despair, or at least a person in this.

Aleuna Macarenko:

What is the name of this church in Avenne (in present-day Belgium)?  I tried to find it on Google but was not successful.  From the stylistic point of view, your capitals appear to be rather rustic for the time range you provide, from 1140 to 1170.  I wonder if the date can be ca. 1140 at the latest?

In the Romanesque and early Gothic context, the beard-pulling images may have simpler meanings as this web site can suggest with a number of sculptural examples: < http://www.beyond-the-pale.org.uk/beardpullers.htm#top >.   I let you go over this interesting website, and judge it for yourself. 

http://www.beyond-the-pale.org.uk/beardpullers.htm#top

By the look of these images there seem to be a number of sub groups within these images that suggest that there is no such thing as a single interpretation of beard pulling figures.

Perhaps the most interesting is the Brive example which is reminiscent of the 'Gripping beast' imagery, it really reminds me of the 'Little Snoring pendant'.

Those dividing their beard in two or similar in style to the Eyrarland image.  A further similar image to the Grain image must be the Sheelagh na Grig tradition of Ireland, although in this case it is a man exposing himself by opening his beard rather than a woman pulling apart her genitals.  It does look as if Campbell's suggestion that these are sexual in nature is confirmed and also that these images continued in widespread use.

However, a great many of these images probably do not belong in this tradition since they appear to depict two figures in combat, I have seen similar in unarmed combat training and street fights many times.  The Gluges figure may represent a sub group of this depicting a man being lead  offo execution.