As a practical matter, the DBs carried by most gyms do not lend themselves to using a weight-based approach to measuring progression on lateral raises, because the weight-intervals available are simply too great. Consider: Going from work-sets with the 15s to the 20s on lateral raises represents an increase of 33%. That would be akin to, say, increasing one's work-set weight on bench-press from 300 to 400 pounds--not something most would attempt. For purposes of doing laterals, it would be nice if gyms carried DB weights of 10s, 10.5s, 11s, 11.5s, etc; but this is impractical. (Although IIRC, magnetized doohickeys can be purchased that allow one to increase the weight of a DB in <1# increments.)
Be that as it may, 'progression' need not be thought of only in terms of how much weight is lifted. With respect to getting bigger/stronger, it's better to think in terms of power than weight. With regards to weightlifting, power can be defined as
Power = Work/time,
where 'work' is defined:
Work = Weight x reps.
Putting them together, we see that
Power = (Weight x reps)/time.
As the equation makes clear, power output can be increased by either a) doing more work, or b) doing the same amount of work in less time. And 'doing more work' can be accomplished by lifting more weight for the same number of reps or doing more reps with a given weight.
As discussed above, so far as lateral raises are concerned, increasing power output via increasing weight is often impractical. Thus, one should focus on increasing output via manipulation of the other components of the Power formula; ie, with a given weight, try to get more reps in the same amount of time, OR get the same number of reps, but in less time (ie, with shorter rest intervals).
tl;dr Use a weight you can handle with good form, and progress by getting more reps and/or shortening your rest intervals.
(As an aside, and IIRC, Charles Staley refers to 'density' rather than power in the formulation above.)