Mike Z. answered 08/04/20
Literacy, Language, Learning Disorders, Memory, and Attention (SLP)
I think it's generally a coincidence, if not a factor of how language tends to reflect what it's describing. I doubt anyone was doing anything intentionally, like you mentioned.
I searched EtymOnline, which has always been a fairly reliable and well-researched source. I found the following:
lisp (v.)
sometimes lipse, late 14c. alteration of wlisp, from late Old English awlyspian "to lisp, to pronounce 's' and 'z' imperfectly," from wlisp (adj.) "lisping," which is probably imitative (compare Middle Dutch, Old High German lispen, Danish læspe, Swedish läspa). General sense "speak imperfectly or childishly" is from 17c. Transitive sense from 1610s. Related: Lisped; lisping. Suggestive of effeminacy from 14c.
You asked if there were other examples of speech-sound errors. There are many. They're often called phonological processes. You can follow this link to a chart (https://littlebeespeech.com/resources/pdf/phonological_processes.pdf).
A phonological process is a specific type of error. When we're growing up, we often make speech errors just as a factor of being a child and not having the auditory acuity to differentiate certain sounds and/or the ability to coordinate the articulators to produce the sounds. It's normal.
But. Some children, for a variety of reasons, may not grow out of these "processes". If they pass a certain age and/or if the errors are just too excessive, we may diagnose the child with a phonological process disorder.
This is different than an articulation disorder, which tends to be a factor of mechanical movement and structural features, e.g., an oral tongue tether/tongue-tie that literally prevents you from articulating, for example.