Patio Grade and Lawn Grade

1/2 inch is a bit too much if you are using sand as a filler in between your payers but not if you use stonedust and landscape paver edging. rain erosion would be more prevalent with a steeper slope of course. so to preserve your hard work, it is probably worth the effort to to use a 6 inch base of crushed stone at 1/4 in slope followed by 1-2 in of stone dust and a finishing sweep of stone dust after the pavers are laid. the 6 in base will also help assure you don't get frost heaves that will loosen the pavers.

Thanks for the reply!

If I do 1/4 inch grade, the end of my patio will be about 4 inches higher than the lawn. What should I do about the sides of the patio to keep everything in place?

Plastic snap edging is the way to go. just drive in 8 in landscape spikes to secure these retainers then backfill with topsoil or gravel right over them. the grass will also root straight thru the openings.

You can also use plastic brick stop edging like this:

1/2 inch per foot is way too much slope for a patio regardless of what you use to install it and it's going to have an obvious slope. If you try to put a 5 ft table on it, one end is going to be 2 1/2 inchs lower than the other and it's going to be obvious something is very wrong. A slope of 1/8 to 1/4" per foot is typical. If you go with 3/16, that cuts your delta at the far end down to 3 inchs. Then I would either use a 3 ft wide planting bed for shrubs, flowers, etc for the transition, or else change the grade of the existing grass over the next 5 ft of so by renting a sod cutter and adding topsoil. If you go with the planting bed idea, you can use a couple large stepping stones in the bed spots you want to use as walkways.