oops -- that's not the USB key! that's my internal m.2 drive!

The partition table is gone, but it used to contain 2 partitions, both of them in an LVM, one of them part of an extended logical volume that added space to /home on my overburdened main drive. I haven't lost much data (just the first 700mb were overwritten), and amazingly my laptop continues to run just fine -- even though lvscan reports a missing drive, apparently the data is still findable. 

I'd like to restore the partition table but I don't know where the partition boundaries are, and in any case I don't know how to write a partition table (!). What tools should I use? Preferably without turning off my laptop, since I'm afraid it won't boot back up again!