Read the label but the longest you have to wait after spraying to replant is 7 days. It is absorbed through foliage and not the root system so your crepes should be fine.

If you're wanting to turn the areas into beds, you could just go with the 'smother with newspaper' route. It takes little effort but requires a bit of patience. I think after laying the newspaper, compost and mulch you have to wait 6 weeks or so before digging through. The time required is shorter in the summer and longer in the winter.

Here is a link that might be useful: Newspapering the Lawn

My 2 bits' worth:
Skip the landscape cloth. It doesn't keep the weeds away after the first season. Some soil will settle on top of the cloth, and weeds will grow in that. Or tiny shoots will come through.
Better to mulch heavily, 4 to 6 inches thick. By all means, use a newspaper to smother the grass, then pile the mulch on top.
You could plant the crape myrtle, leaving some space around its root ball open, and newspaper & mulch beyond that space. You will still have to pull some grass/weeds out close to the crape myrtle, but you would need to do that occasionally no matter which technique you use to suppress the weedy lawn.

Stpete is right. I meant to touch on that as well. From everything I've been reading, the only thing Weed/Landscape cloth is really good for is burning a hole in your wallet. It doesn't last and it doesn't prevent weeds any better than newspaper (it may even be worse). And when the landscape cloth tears and breaks down, it provides nothing to the soil underneath, it just makes for a big job further down the road as you have to pull it up and replace it. Newspaper breaks down over time, feeds the soil and attracts earthworms, which then eat the newspaper, turning it into free fertilizer! Cardboard is another option, but it takes longer to decompose and is harder to cut through if you want to put in a plant. If I pulled up all my mulch, there would be a jigsaw of newspaper and cardboard in my beds. I tried putting the cardboard in areas where I was fairly sure I wouldn't be putting any plants and put the newspaper down in the spots where I might some day install a shrub or something.

I recently smothered my front lawn and put in native bushes and plants. I found the easiest way to smother it was with the brown paper you can buy in big rolls at lumber yards. It's fairly inexpensive, and doesn't blow away like sheets of newspaper in the slightest wind. Once the brown paper was down, I covered it with about 4 inches of wood chips.

You may also be able to get large cardboard from furniture/appliance stores. Just be sure to remove any tape or staples. I wouldn't use landscape fabric or plastic either.

Whichever method you use to get rid of grass, the soil likely won't be capable of producing great plants the first year. I would do as recommended, plant some larger things and smother around them, covered with mulch. If you're anxious for some smaller plants, potted annuals sitting atop the mulch could be a good compromise for this year. When you dig in next spring, you should be pleasantly surprised by the difference, the cardboard should be gone unless it rarely gets wet.