Sounds like you need a table.
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If every line is a new paragraph, you can set up two paragraph styles — one with the paragraph rule and one without. In each one, set the other as Next Style.
The select all the text, and right-click (or option-click) on the style for the first line, and choose Apply Style, then Next Style.
You could also turn the whole thing into an InDesign table, and use alternating fills.
Thanks, I used a table