On the IPA consonant chart they are greyed out as impossible to occur. But I can easily clamp my tongue between my lips, or I can close only the center of my lips, either way leaving a narrow hole on both sides. So they seem very possible.
The Handbook of the International Phonetic Association says (p. 9):
Shaded cells occur where the intersection of a manner and a place of articulation define a sound which is thought not to be possible, either by definition (a nasal requires an oral occlusion combined with lowering of the velum, and so a pharyngeal or glottal nasal is ruled out), or because the sound is impossible or too difficult to produce, such as a velar trill or a bilabial lateral fricative.
So bilabial laterals apparently fall under the "impossible or too difficult to produce" category. I think I agree with you, in that the shading seems a bit overreaching, or "impossible or too difficult" needs clarification. Other sounds that are physically possible but shaded in the IPA chart include pharyngeal laterals and velar taps. It looks as though whether the sounds would be acoustically distinct, or how likely they would be used distinctively in a language, is also taken into account in deciding which cells to shade.
Peter Ladefoged discusses the difficulty of determining what can and cannot be a speech sound in an interview by Victoria Fromkin (Fromkin 1985: 11):
PL: It's awfully difficult to say why a particular sucking or popping noise is or is not a speech sound except to say that it is comparatively unnatural, which means that it's a little more difficult to make in some kind of way. But think of all the speech sounds that are difficult to make, which shows that the difficulty criterion is not very helpful. [...] Anybody can make a sound consisting of putting the tongue between the lips and moving it rapidly from side to side. It seems to be very easy to do. But no language—or none that has yet been found—has the sound produced in this way.
VF: Isn't that what we used to say about bilabial trills?
(I suspect the "clamping" articulation you mention would be considered linguolabial, by the way.)