MED offers two citations in which lyspynge is glossed blesus or blesura, which is clearly cognate with wlisp-.
According to Lewis & Short, blaesus means "lisping, stammering, hesitating in utterance, speaking indistinctly" (giving a citation however corresponding to the modern sense of defective sibiliance: blaesus, cui litterae sibilantes (s, z) molestae sunt vitioseque pronunciantur, Popm. Differ. p. 133). Blaesus is there derived from Greek βλαισός, which the "Greek Word Study Tool" at Perseus defines thus:
A. bent, distorted: hence, splay-footed, Hp.Art.53, cf. 82 (Comp.); ἐς τὸ β. ῥέπων ib.62, cf. Gal.18(1).674, al.; “οἱ β. τῶν ἀνθρώπων” X.Eq.1.3; also, bandy, “β. καρκίνοι” Batr.297, cf. Arist.HA526a23; τὰ β. τῶν ὀπισθίων the hollow of the hind-leg in which bees carry the pollen, ib.624b2: generally, twisted, crooked, “πλατάνιστος” AP4.1.17 (Mel.); κισσός ib.7.21 (Simm.).
So the root sense seems to be "distorted" or "twisted".
On the other hand, one variety of lisp subsitutes a lateral "l-coloured" consonant for the sibilant, and in my mouth the /wl/ seems to exert some pressure toward that sort of pronunciation of the following /s/. It is easy to conceive that this might support an extension of a word meaning "twisted, stumbling (legs)" to "twisted, stumbling (speech)".
It may be coincidence, but in the Ystoria Taliesin the magical child-poet charms King Maelgwn's bards by pouting out his lips and playing "Blerwm, blerwm" upon them, so that they are incapable of verse but can only play "Blerwm, blerwm" on their lips likewise.