If (as you indicate) your standard style for a simple citation takes the form "(Source at 5, lines 10–14)," then it seems to me you are bound to extend that form to more-complicated citations, such as "(Source at 5, line 20, through 6, line 2)." Otherwise, you are, in effect, demanding that readers learn two short citation forms that will appear interchangeably in the book. But the ungainliness of the complicated citation's form isn't really the fault of the complicated citation; it's the fault of the underlying simple form.
One of the short-form text citation examples in the 15th edition of the Chicago Manual of Style (at 16.109) involves multiple page references within a particular source. Here's the relevant section:
16.109 Page numbers or other specific references. When a specific page, section, equation or other division of the work is cited, it follows the date, preceded by a comma.
[Examples:] (Piaget 1980, 74) (Johnson 1979, sec. 24) ((Fowler and Hoyle 1965, eq. 87) (Barnes 1998, 2:354–55, 3:29) (Fischer and Siple, 1990, 212n3)
Following the "(Barnes 1998, 2:354–55, 3:29)" form above, you could consistently indicate the relevant pages and lines of your citations by adopting the form "(Source, page:line)." In the usual simple case, this would yield short-form citations that look like this:
In the more complicated cases, it would yield entries such as this:
Because a lowercase l looks so much like a 1, I would not add an "l" element to the short form, to avoid making the citations unduly confusing to readers.
The crucial thing in adopting any specialized short-form citation style is to make clear to readers what the elements of the short form are. This is especially true if your short-form style isn't standard at your publisher or in your discipline. The simplest way to introduce such a form is in a note at the beginning of the long-form bibliography, where readers will go in any case when they want to identify a citation in full.