Cold infusion requires more time to infuse, but that can be easily done overnight: fill a 1L jar or pitcher with 2-4 sprigs of rinsed, freshly picked lemon verbena (or spearmint, or 4 blades of lemongrass). Cover with spring water or tapwater (filtered if necessary), and let it sit overnight in the refrigerator. In the morning, you'll have a cool, refreshing beverage, which you could fill in your to-go bottle, while covering the herbs again with fresh water for a 2nd cold-infusion.
When cold-infusing fresh lemon verbena leaves, the result is a more grassy, green and delicate infusion. The citral is a little less dominant as well, giving more room for the more floral and green notes. Also, the result is a very clear water, which is most refreshing in the hot summer months. We drank lemon verbene, spearmint or lemongrass infused water all summer and they were thirst-quenching and provided little moments of sanity and a pure luxury while hydrating.
Making a hot infusion is wonderful too - and will bring out the bright yellow colour of lemon verbena. It will, however, require more planning ahead: You'll have to infuse the tea, bring it to room temperature, and than chill it for at least 4 hours, if not overnight (depending on how much power you have in your refrigerator: the one we had in the village was an ice-box size machine with very little cooling power, so everything had to be planned and thought-through well ahead).
I was first introduced to this method by my Canadian-Japanese friend Dean, who would make cold barley "tea" every summer (it's a simple infusion of roasted barley, that is very popular in Japan in the cooler months; you might be also able to find cans of this treat at the Japanese Konbiniya on Robson street - or your own local Japanese/Asian grocery store). Second time I learned about it was from Maria at Shaktea on Main: she recommended this method for making iced tea from their aromatized white and green teas (their Pomegranate & Magnolia was my first time experimenting with this method, and their Elderflower & Cantaloupe is even better this way). It might be a bit tricky with aromatized teas though: the aromas can taste a bit plastic-y and tongue-burning sometimes if they don't udnergo the heating. So you will just have to test and see for each tea if that method makes it better or worse than cooling a hot-infusion. Like the cold infusions of fresh leaves, dried tea infusions may be re-steeped a 2nd and even a 3rd time.