I found a website that is helpful for studying Japanese.
In Hungary there is a proverb meaning, "Running away is a shame, but it's useful."
Would a sword be more useful than a gun for walking through a city full of zombies?
When you stand up to do your duty you're standing up and finally being useful. That's why this verb means to be useful.
The reading for 役 is the one you learned with the kanji. The 立つ reading is that of the 立つ vocabulary, which you should be familiar with by now.