I'm picturing a vertical tree structure like one would see in an OS file browser (see below). Is this right?
Stripes can Improve Usability
I think horizontal stripes (or lines) can help, but the help they provide is most beneficial when dealing with a horizontally large tree or list. For example, in the image above, if I need to connect a file name on the far left to a file size on the far right, the stripes help my eyeballs stay on the right line and connect the bits of information I want.
But Keep It Subtle
If you're using the lines as a "helper" like this, I would take the time to seriously design them properly to balance their contrast with other higher-level interface actions. For example, don't make them pure black on pure white (the stripes will be hard to read between). Instead do something like an alternating background color for each row of the tree/list and make that color have only just enough contrast that you can see it (and use it) but no more (so as not to interfere with more important parts of the interface).
Stripes May Not Be Necessary
If the list is mostly vertical and relatively horizontally compact, the lines might not be that helpful and may only be cluttering the interface. For example, below is an example of the file browser for a project in my code editor. Without the added complexity of lines or stripes, this vertically-oriented list is easier to scan:
Keep All Elements in Balance
This is a really subtle part of the design and should really be a lower priority to the primary actions of the application that's being designed. Everything in the interface needs to be balanced and weighed against everything else for both utility and aesthetics.
EDIT: Vertical Lines
Vertical lines can play the same role as horizontal lines in that they enhance the user's ability to navigate tables of data with his or her eyes, but they're not absolutely necessary, and should always be balanced with the design's visual hierarchy. Below is a screenshot I took from Adobe's Livedocs and modified to illustrate alternative approaches and how they work side-by-side.