Who are the people Isaac Watts is talking about in "Improvement of the Mind"?

TL;DR: These are fictional types, not real people.

Take your first example with a little more context:

A Man much addicted to Luxury and Pleasure, Recreation and Pastime, should never pretend to devote himself entirely to the Sciences, unless his Soul be so reform’d and refin’d that he can taste all these Entertainments in his Closet, among his books and papers. Sobrino is a temperate Man and Philosopher, and he feeds upon Partridge and Pheasant, Venison and Ragouts, and every Delicacy, in a growing Understanding and a serene and healthy Soul, tho’ he dines on a Dish of Sprouts or Turnips. Languinos lov’d his Ease, and there chose to brought up a Scholar; he had much Indolence in his Temper, and as he never cared for Study, he falls under universal Contempt in his Profession, because he has nothing but the Gown and the Name.

_{Isaac Watts (1743). The Improvement of the Mind, p. 14. London: J. Brackstone. My emphasis.}

The first sentence is a little moral homily about the proper behaviour to be adopted by scholars. Then the next two sentences are (fictional) positive and negative examples. The name Sobrino is modelled on Italian sobrio meaning “sober, temperate”; the character follows the advice, and prospers. The name Languinos is modelled on Italian languido meaning “languid, indolent”; the character neglects the advice and declines.

In your other example, Lucidas is modelled on lucido meaning “bright, shining” and Scintillo is modelled on scintilla meaning “spark”. Their names suit their characters:

Lucidas and Scintillo are young Men of this Stamp: They shine in Conversation, they spread their native Riches before the Ignorant; they pride themselves in their own lively Images of Fancy, and imagine themselves Wise and Learned; but they had best avoid the Pretense of the Skilful, and the Test of Reasoning; and I would advise them once a Day to think forward a little, what a contemptible Figure they will make in Age.

_{Watts, p. 11.}