Keep out of sight; bide one's time.

There are many citations of variants of this little phrase dating back to the 13th century. Shakespeare used it in its present form in Much Ado About Nothing, 1599:

ANTONIO:

If he could right himself with quarreling,
Some of us would lie low.

More recently the phrase has been adapted as the name of inflatable mattresses - marketed in the UK as Li-Los.