It's certainly easier if you have a friend/significant other who can help out (makes the initial outlay cheaper too if you go in on a lactate tester with a training buddy or 2 and agree to test each other!)

But you can definitely do it on your own if you organize beforehand, especially if using aerobars for the test:
* Set up a table to the top right corner of the bike (assuming right-handed)
* Lay out alcohol swabs already opened
* Have test strips lined up at the ready
* Have a stack of gauze pads

For each stage - alcohol wipe -> spike finger -> gauze wipe -> sample

When sampling, hold the tester like a pencil i.e. with the strip pointing down into the blood droplet. Capillary action of the strip will suck the blood up.

Movement isn't usually too much of a problem, especially on the aerobars, until the effort gets close to maximal. At that point, a 2 second pause in pedaling to get the sample won't throw things off too much.