How can I create a pattern of parallel lines that are increasing in distance in Photoshop / Illustrator?

Use Blend and Clipping Masks!

1. Make a text by text tool and write anything!

2. Press P to select pen tool and draw simple line (you can use line tool too).

3. Remove Fill and Give Stroke to the line eg. 4px.

4. Duplicate your line and drag it down and reduce stroke to very less eg. 1px;

5. Go to Object → Blend → Blend Options and change spacing to Specific Steps and enter value like 30 steps or so.

6. Select both layers and press Ctrl+Alt+B or go to Object → Blend → Make.

7. Extra: You can expand blending and make group if you want by Object → Expand and you can edit your blending however by moving it’s child objects by direct selection tool!
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8. Move your blending to the bottom of your text Layer. to do so just select your blending group and press Ctrl+Shift+[

9. Now all you have to do is select your text and blend altogether and Right click → Make Clipping mask and see magic happening!