Ideally, you'd have edging on both sides of the fence -- even if you didn't plant on both sides. This would help your mowing -- if the edging was flush with the ground, you could just run the mower along the edge and be done.

One thing to bear in mind is that exposing the soil to the sun also exposes weed seeds to the sun. If you get enough rain that the seeds sprout, there will be no shade to prevent them from taking root. You might scalp part of the lawn and leave part unmowed. Then write back in July to tell us what happened.

"There is no chemical treatment for dallas grass other than Roundup and hand digging." Well, actually there IS a chemical treatment for dallisgrass (not dallas grass), but it cannot be used on perennial ryegrass. Monosodium methanearsonate (MSMA) is labeled for use on home lawns for controlling dallisgrass in established bermudagrass, zoysiagrass, and bluegrass.

You need to remove the metal edging. Kimmsr is correct, there is no effective barrier. Any form or artificial edging will just give you a false sense of security. you then need to cut in a deep v shaped trench along the line in your photo. Hand weed out the grass in the tree bed. Religiously maintain your cut edge to the lawn. Trim it once a week without fail, preferably with sharp long handled lawn edging shears. Here is a link that might be useful: Bahco Lawn Edge Shears