The concept of Infinity is used several times throughout the series. In addition to the repetition of the number 8, this seems symbolically tied in with the central themes of the books. The lemniscate first appears in the workbook given to the sisters by their mother. The fact that the concept of infinity is discussed in the book suggests that it is not a workbook for fourth-graders. It seems it is either a very advanced textbook, or their mother created it specifically to prepare them for something.
The concept is explained by Jackie in relation to 'living forever', and counting during the duration of the entire life. This is significant, as the misconception that their mother is working on the secret of 'eternal life' is central to the series. It would seem that her true work is something more theoretical, and possibly mathematical.
Though the number 8 is unquestionably significant in the story, infinity is vital to understanding the narrative at a deeper level. The ninth book takes place in another universe. The Greek philosopher Anaximander, one of the first to unite the concept of the Infinite or Boundless with philosophy, also had a notion about multiple or possibly infinite other worlds. A Roman thinker thought that the Mind was infinite. Since some of the Eights' powers are certainly telekinetic, this seems incredibly significant.
The lemniscate is also a symmetrical shape, tying into the central theme of Symmetry in the series.