Where I’ve seen the DL123 used is in camera where the drain would generally be fairly low but when using the flash there would be a high current pulse and that’s probably why they have the pulse rating of .9A, 3sec on, 27 sec off. It could also be used in LED flashlights of moderate drains. Using it in high power flashlights or other applications where it would have a 1000Ma drain would cause the initial voltage under load to be about 2.5 instead of 3.3 and it would only last 1 hour. Single use batteries like this aren’t that practical for high energy applications because of the higher cost for a short life. The maximum continuous rating is for a typical use where you would use it on for some longer period of time and the maximum drain is the maximum safe allowable drain under any conditions. Try to draw more current than that and bad things may happen including overheating or violent battery failure.
If the DL123 is used in low drain applications it will last a fairly long time and in smoke detectors I’d expect it to last a couple of years and still be o.k. when you replace it as recommended for safety reasons
It looks like if 3.3VDC would work for your small scope the DL123 would last about 10 hours. If you don’t need it to be portable I’d suggest a line operated power supply so you don’t have to worry about the charge left in the battery.
Note: I just checked the specs and it looks like the DSO138 will operate from 9-14 volts so one DL123 battery won't work unless you use 3 cells or one cell and a DC-DC converter, which, because of less than 100% efficiency, would further shorten battery life. Google DSO138 and battery and you can get some ideas what others have tried.