From the Earliest Known Uses of Some of the Words of Mathematics site :
PENCIL OF LINES. Desargues coined the term ordonnance de lignes, which is translated an order of lines or a pencil of lines [James A. Landau].
Boyer's A History of Mathematics (1968, p. 396) also attributes this terminology to Desargues. From the section on Blaise Pascal, when discussing his Hexagrammum Mysticum Theorem :
... he followed the special language of Desargues, saying that if $A, B, C, D, E,$ and $F$ are successive vertices of a hexagon in a conic, and if $P$ is the intersection point of $AB$ and $DE$ and $Q$ is the intersection point of $BC$ and $EF$, then $PQ$ and $CD$ and $FA$ are lines "of the same order" (or, as we should say, the lines are members of a pencil, whether a pencil point or a parallel pencil).
The intuition behind the choice of pencil in the English translation is not entirely clear. Perhaps "order", as in the translation "an order of lines", was already too strongly associated with order. Boyer hints at this translated usage, writing :
[Desargues assumes] that the parabola has a focus "at infinity" and that parallel lines meet at "a point at infinity". The theory of perspective makes such ideas plausible, for light from the sun ordinarily is considered to be made up of rays that are parallel - comprising a cylinder or a parallel pencil of rays - whereas rays from a terrestrial source are treated as a cone or a pencil point. The cylinder is merely a cone the vertex of which is infinitely distant, and a parallel pencil of lines is simply a family of lines all of which go through the same point at infinity. Desargues similarly studied a sheaf or bundle of planes through a point, finite or infinite.
Reading further, it appears that Desargues was fond of colourful terminology. For example, he calls a conic section a "coup de rouleau" - i.e., incidence with a rolling pin.
Also worth considering is that Desargues introduced these ideas and terms in a work not translated for at least two hundred years after its first appearance. Desargues' Brouillon Projet d'une atteinte aux événements des rencontres du Cône avec un Plan (trans: Rough Draft of an Attempt to Deal with the Outcome of a Meeting of a Cone with a Plane) first appeared in Paris, 1639. According to Boyer, Desargues published his works not to sell but to distribute to friends. The work was completely lost until in 1847 a hand written copy made by Phillipe de Lahire, one of Desargues' few admirers, was found in a Paris library. Brouillon Projet is described by Boyer as one of "the most unsuccessful great books ever produced".