Yes, you can. Lash extensions are affixed to your natural lashes, and when properly applied, do not touch the eyelid skin.
Strip lashes are applied to the eyelid, at the base of the natural lashes.
The issue with applying strip lashes when wearing lash extensions is if one uses an excess amount of lash adhesive and applies the lashes while the adhesive is still wet, the adhesive will seep out from under the lash band onto the natural lashes and lash extensions, and dry. Then, when one removes the strip lashes, it’s likely they’ll pull off some of the lash extensions (and pull out some of their natural lashes as well).
From what I’ve observed viewing dozens of YouTube videos in which strip lashes are applied, most people use far too much lash adhesive and apply the strip lashes while the adhesive is still too wet.
Temporary lash adhesive is similar in composition to rubber cement*, an adhesive used to create a temporary bond with paper. Rubber cement, when properly used, allows one to separate the papers later without damage.
As when using rubber cement with paper, temporary lash adhesive should be applied sparingly to the lash band and be allowed to “dry until tacky” before applying the lashes to the eyelid.
How long it will take for the lash adhesive to achieve the “tacky” stage depends upon how much adhesive is used, and the temperature and humidity in the room in which the lashes are being applied.
To learn how to determine when the adhesive has achieved the “tacky” stage, take a cheap pair of lashes and apply a thin, even layer of adhesive to the band using a toothpick. Observe how the adhesive changes in opacity as it dries (out of the tube it’s opaque. When completely dry, it becomes almost transparent). Make note of how long it takes to completely dry.
Then repeat the experiment. This time, when half the time has elapsed between applying the adhesive and the adhesive being completely dry, make note of how the adhesive looks at that stage, then apply the lash to the back of your hand.
If the adhesive is at the “tacky” stage there should be an instant bond (the lashes shouldn’t slide around and you should not be able to reposition them). There should be no oozing of adhesive from under the band.
If the adhesive oozes and the lashes can be repositioned, then you’ve used too much adhesive and have applied the lashes too soon.
Keep practicing until you’re able to visually identify when the adhesive has reached the tacky stage.
Once you’re able to do this, then you can wear strip lashes with (or without) lash extensions without damaging the extensions or your natural lashes.