The acceptability of the use of footnotes varies a lot. 6-7 lines would be huge in many works but is nothing when compared to others.
If it doesn't belong inside the text, and endnotes aren't a possibility, then a long footnote seems appropriate. I would cut it down as much as you can.
Footnotes should be more informational than storytelling. While you might not think of your paper as using storytelling, it does (or should). Think of the difference in a scientific paper between the body of the paper and the abstract. A paper written entirely like an abstract would be boring and hard to read. But an abstract written like a paper would be too long and hard to skim. Footnotes should be more like an abstract.
In some cases, footnotes can be longer than the rest of the work! It all depends on context. I keep thinking of Pioneer Girl: The Annotated Autobiography. This enormous volume has the text of Laura Ingalls Wilder's 9 primary books. Every comment, fact check, historical mention, and additional photographs, etc is done in footnotes (they are in the outside margins, not the bottom). You could not have added these to the text directly and endnotes would have been crazy making. The only option is footnotes or some other side-by-side rendition.
Since you're not annotating, if you find that your footnotes as a whole take up a large percentage of space in your paper, I would recommend that you find a way to incorporate them into the text. Footnotes should be for citations and short additional bits. One longer addition is fine. Several is probably too much, depending on context.