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.
Words whose sounds refer to, suggest, or otherwise are associated with a particular meaning are cases of sound symbolism. Although onomatopoeia - direct imitation of a real-world sound - is one type of sound symbolism, it is not the only one.
A common sound symbolism is sound iconism. With the related clustering, this is the re-use of sounds across a set of words with related meanings. Note that this is the re-use of sounds, not morphemes. One example is found in the set of words stamp, stomp, tamp, tromp, and tramp which have the common /-mp/. The final /-mp/ sound is strongly suggestive of stomping or stamping, though it's actually not imitative of it.
Another set of words is glisten, gleam, glint, glare, glam, glimmer, glaze, glass, glitz, gloss, glory, glow, and glitter. The /gl-/ is associated with shining, though it's not imitative in any way since shining is visual, not auditory. Nevertheless English speakers hear these words as related.
This is not unique to English of course. For example, in Japanese linguistics one finds the terms phenomime and psychomime for similar phenomena.
Best Answer
It's not onomatopoeic in the normal sense, since onomatopoeia describes a word which mimics the thing it stands for. Unless hooray can satisfactorily be construed to mimic anything but itself and its own variants, it doesn't count as onomatopoeia. For instance, if it were possible to know that hooray did not descend from a word, and did descend from a natural and common noise, then it would be onomatopoeic.
On the surface, Wikipedia seems to favor the onomatopoeia hypothesis:
But even while it states that it is "probably onomatopoeic", it goes on to feed the other viewpoint, namely that hurrah did in fact originate from an arbitrary word, and therefore is not onomatopoeic.