Actually, the best scenario would be the #14 lottery team getting the #1 pick.
The drawings for the first three picks happen in order: #1, #2, #3. Atlanta, just like every other team (still) in the lottery, goes into the hopper for each of those picks in succession. For the #1 pick, Atlanta is the fourth most likely team to get it. For later picks, Atlanta's chances depend on who else is left in the lottery. The Suns want Atlanta to have as much competition as possible for the #2 and #3 picks. If the #5 or #6 team moves up, that thins the field a little for the next lottery pick, slightly improving Atlanta's chances.
The real numbers are messy, but the point can be illustrated with simplified numbers. Let's say there are 10 lottery teams, with the #1 lottery seed having 10 chances, the #2 seed having 9, and so on down to the #10 seed having 1 chance. That's 55 total chances. In this example, Altanta has 7 chances, so they have a 7/55 = 12.7% chance of winning the top pick.
If the #1 team wins the top pick, their 10 chances are removed for the rest of the lottery. Now there are only 45 chances left for the #2 pick, of which Atlanta has 7, or 15.6%.
If the #5 team wins the top pick, their 6 chances are removed. Atlanta has 7 of the remaning 49 chances, or 14.3%.
If the #10 team wins the top pick, only their 1 chance is removed. Atlanta has 7 of the remaning 54 chances, or 13.0%.
No matter who gets #1, if it's not Atlanta, Atlanta's odds for #2 improve. The question is by how much. Then the same thing happens for #3. Only after all three picks have been assigned to other teams are the Suns in the clear.