Don't fall behind our competitors.

Literal

Other-companies [to-に] lag [object-を] take-[prohibitive-な].

A blunt workplace directive. The sentence-final な here is the prohibitive (not the reflective), attaching directly to a dictionary-form verb to mean 'do not X.' This is the most brusque form of negative command in Japanese, used primarily in authority-down contexts: workplace, military, sports coaching. 後れを取る ('to take a lag,' 'to fall behind') is a set idiom for being outpaced or surpassed by someone. 後れ (遅れ) is 'lateness, lag,' and 取る here functions as the light verb 'take on, acquire.' Common in competitive contexts: 時代の波に後れを取る ('fall behind the times'), ライバルに後れを取る ('fall behind a rival').