Yes, you can measure your intraocular pressure with al Reichert tonometer while lying down. The Reichert 7CR model works best, and I have done it long enough to feel comfortable that it does not harm the tonometer.
Here is a photo I posted in 2010 of my Reichert 7CR:
I find it very easy to take an "upon awakening" IOP measurement without sitting up at all. I don't even have to lift my head.
If I am sleeping on my right side, I simply stay on my right side and take the measurement. I have even taken IOP measurements while still half-asleep (and slightly dreaming).
If I am sleeping on my left side, I so have to roll over to my right side, but I do not even have to lift my head off the pillow.
I do not have to change my head position to measure both eyes. As the photo shows, there is a small pillow under the head end of the tonometer. This elevates the tonometer and allows me to measure the left eye. When done, I simply slip the pillow out from under the tonometer and I measure the right eye.
Because I am using the free FitEyes software to take the measurement, I do not even have to fumble for the tonometer buttons or do anything else that requires attention. This is how I can take measurements while half asleep. I can even take measurements in the dark this way.
I believe FitEyes was on the forefront of bringing awareness of just how fast and how far IOP can drop in the first moments after getting out of bed. Many FitEyes members with tonometers see IOP drops of 5mmHg (or more) in about 60 seconds after getting out of bed. Even larger drops in IOP are possible.
In addition to this. I have seen IOP change as I transition from the sleeping state to the awake state, even without changing my body position.
In my opinion, the most important measurement anyone with a tonometer can perform is this "upon awakening" measurement while still lying in bed, as I just described. As Dr. Ritch says, you shouldn't even sit up for a minute before you take the measurement.
However, I have found that if I do sit up for a moment, if I lie back down for a few minutes and then take my IOP while lying down, it seems close to the value I would have expected had I not briefly sat up. However, I prefer not to do that because it introduces a question mark into the data. My normal routine is to take my IOP without ever lifting my head off the pillow, and that's how I do it 99.9% of the time.
The only slightly tricky things I have encountered are:
I need to carefully position my right arm so that it doesn't restrict my breathing when I am on my right side. I simply make sure I am comfortable as I slide my head up to the tonometer.
I need to have the right type of pillow for my head so that my head will be at the proper level. Since I already had satisfactory pillows, this is very easy. I use a buckwheat pillow.
My relationship to the tonometer is the same as when I am sitting up and it is sitting up. In bed, I am on my right side and the tonometer is on its side. I still look directly into the tonometer as I would when sitting up. And taking a measurement is the same. The process works well when you have your pillows situated correctly.
If you want to read my original 2010 post, find it at this link:
If you have an iCare tonometer, please see this answer:
How do you measure your eye pressure with an Icare tonometer while lying down? | Ask FitEyes