Probably the easiest is to have a lot of variables as follows. Pos is a value from 0 to 1 that when used with lerp can give an angle between the start and end angles.
--> add dt to pos
---> set pos to 1
---> set angle to anglelerp(start_angle, end_angle, pos)
Start of layout
---> set start_angle to 0
---> set end_angle to 90
---> set pos to 0
That's the long version. You can simplify it but it becomes less readable.
The "start of layout" condition is an example how to use it. You need to set the start and end angles and reset pos to 0.
Also the transition will take one second. You can make it faster or slower by adding another value to "pos".
2*dt for 0.5 seconds
0.5*dt for 2 seconds
0.1*dt for 10 seconds
Finally it's a linear angle change, although you can make it ease in-out by changing:
anglelerp(start_angle, end_angle, pos)
anglelerp(start_angle, end_angle, cubic(0,0,1,1,pos))