Um instantâneo LVM só precisa de tanto espaço quanto é diferente do LV original. Portanto, se você criar um instantâneo LVM de um volume de 1.0 GB, o tamanho do instantâneo será 0 (bem, exceto alguns metadados, eu acho). Se você está alterando dados no LV original, digamos que você baixou um arquivo de 200MB, o instantâneo do LVM seria de 200MB. Se você definiu o tamanho do instantâneo para 2 MB, esse instantâneo seria inutilizável porque não poderia gravar os 198 MB restantes.
Extraído do manual:
-s, --snapshot
Create a snapshot logical volume (or snapshot) for an existing,
so called original logical volume (or origin). Snapshots pro-
vide a 'frozen image' of the contents of the origin while the
origin can still be updated. They enable consistent backups and
online recovery of removed/overwritten data/files. The snapshot
does not need the same amount of storage the origin has. In a
typical scenario, 15-20% might be enough. In case the snapshot
runs out of storage, use lvextend(8) to grow it. Shrinking a
snapshot is supported by lvreduce(8) as well. Run lvdisplay(8)
on the snapshot in order to check how much data is allocated to
it. Note that a small amount of the space you allocate to the
snapshot is used to track the locations of the chunks of data,
so you should allocate slightly more space than you actually
need and monitor the rate at which the snapshot data is growing
so you can avoid running out of space.