General:
* A series of lines
* A set of lines
* A collection of lines
* A network of lines
* A tapestry of lines
Specific:
* A grid of lines (for parallel lines)
* A tangle of lines (for messy or interwoven lines)
* A constellation of lines (for lines arranged like stars in a sky)
* A symphony of lines (for lines that create a harmonious or artistic composition)
Ultimately, the best collective noun will depend on the specific meaning and context of the lines in question.