I don't have lattice, so I don't know what will grow well on it, but if you run string down in front of it, most any vine will grow up string and you can choose a biodegradable twine that at the end of season you can just rip out and compost along with the vines. Two of my favorite annual vines are Thunbergia alata/black-eyed Susan vine and scarlet runner beans. The beans are edible both as green beans when young and as dried beans when old, and the hummingbirds love the flowers. It will bloom most if the beans are kept picked. Both like at least a half day of sun. You may want to add some shrubby or draping plants to the planter box as well since vines usually aren't bushy at the bottom.

thank you for the suggestions. I do like the black-eyed Susan vine. How many would you suggest I plant given the width of the trellis?

How wide is each panel? 3'? 4'?

Remember when sizing your planter box that a larger box will have more even temperature and moisture, so the plants will be happier. Also, most plants in pots do best with a very dilute (way less than label directions) level of fertilizer each time you water. The folks on the container gardening forum can probably advise you as to good soil and amount of fertilizer and best box sizing.

Not an annual, but I also like Mandevilla vine. It's a tropical perennial, so you would have to cut it way back and transplant to a smaller container to overwinter indoors unless you have a warm garage with a white window and the box is on wheels or you are willing to buy new each year.

I can buy both Mandevilla and Thunbergia at local nurseries that emphasize annuals.

I'd consider sweet peas. They are very easy to grow from seed, won't mind the less than full sun location (in fact, will prefer that), and make wonderfully fragrant cut bouquets. In fact, the more you cut, the more they bloom!!

I figured sweet peas would fade in summer in NJ since they faded here in NH. Am I wrong about that and I am just incompetent at growing sweet peas?

All grand suggestions, above. I have window boxes on the pool deck, that are planted with vines to grow on the lattice fence around the deck. Morning Glory, Cypress Vine, Scarlet Runner Bean, white Hyacinth Bean, Moonflower, all in a blooming mess. Have perennial vines all over the lattice fences behind my tiny rock garden, on the various trellises, and the trellis fence that hides the side of the above-ground pool from where we park the vehicles. If you have time, cursor down to past postings, in my blog, 'Bogturtle's Garden'.

Part of Blogspot, but cannot seem to post URL.

http://bogturtlesgarden.blogspot.com/