There are many options in Rx-Universe to control thickness and thickness tolerances of lenses.
Default Thicknesses
For each job, "default" thicknesses will be determined, based on the power of the lens, the type of frame edge, and the lab's preferences.
On the material screen, the lab can specify the default thicknesses for minus and plus lenses:
The "Default CT" is the center thickness used for minus lenses.
The "ET @ Plano" is the desired edge thickness of a plano lens.
The "Minimum ET" and "Power @ Min ET" go together, since the minimum edge thickness occurs at the specified power.
So in the above example, a plano lens would have an edge thickness of 2.0, and a +7.00 lens a minimum edge thickness of 0.8mm.
The relationship of minimum edge thickness to power is linear, so a lens of +3.50 power would have a minimum edge thickness of 1.4mm. The minimum ET of any power can be illustrated with a graph:
Finished Lenses
When considering finished lenses for blank selection for plus jobs, Rx-Universe will look at each finished lens, and calculate what the final edge thickness will be, for the frame and Rx, using each finished lens. If the lens has an edge thickness within a specified tolerance, then it will be deemed acceptable, otherwise it will be rejected, and blank selection will consider the next possible lens.
Consider, for example, a job with a +2.00 sphere, in a frame similar to the following. The "x" indicates the OC, and the line is the radius to the frame edge furthest from the OC (since the lens is spherical, the longest radii will correspond to the thinnest edge point). 
For discussion, let's assume the system is set up for a default edge thickness of 1.5mm for this job. If the job were being surfaced, the min ET would be set to 1.5mm, and the CT calculated to obtain that edge thickness with the blank being used.
When considering finished lenses, the center thickness is already fixed, so Rx-Universe will take that CT, and using the front curve of the lens, calculate how thickness the lens will be at the thinnest edge point on the frame.
A 65mm finished blank might have a center thickness of 3.30, and result in an edge thickness (again, at the thinnest edge point) of 1.3mm. A 70mm finished blank might have a center thickness of 3.9mm, and result in an edge thickness of 1.9mm (again, at the thinnest edge).
The 65mm blank will result in an edge thickness that is 2/10 thinner than the desired 1.5mm ET, and the 70mm blank will result in an edge thickness that is 4/10 thicker than the desired 1.5mm. Neither lens will give exactly the desired edge thickness, but a lab may decide that 2/10 thinner is acceptable, or that 4/10 thicker is acceptable, or that both (or neither) are acceptable.
How much thinner or thicker a finished lens can be that the desired ET is known as thickness tolerance in Rx-Universe terminology. This can be set system-wide on the "Blank Selection" tab in System Parameters:
Using these settings in relation to our example job, recall that the desired edge thickness was 1.5mm. These settings mean a finished lens could be between 1.2mm and 2.3mm thick at the minimum edge, and be acceptable.
Since Safety jobs often have different rules (they usually cannot be thinner than the calculated minimum), there are separate thinness and thickness tolerance for Safety jobs, as seen here.
Other frame types may also require different settings. Within the frame type setup, the lab has the ability to set different tolerances for the frame type, by material type:
In this example, a groove frame type has different settings for different material types. A poly lens could be up to 2/10 thinner than the 2.2 minimum edge specified for this frame type, and up to 1.0mm thicker. These parameters will change depending on the lab's preference, the equipment being used to groove, the experience of the operator (if doing manual grooving), and what the default thickness is to start with. For example, if a lab wanted the minimum edge to be 1.8mm for grooving, a finished lens probably could not be any thinner.
While the discussion herein discussed minimum edge thickness for plus jobs, the same rules and logic apply to minimum center thickness when considering finished lenses.