PIE base ‘to care, desire; love’.
Other derivatives include believe ‘hold dear, love’, belief, leave ‘permission to do something’, indicating pleasure or approval, furlough ‘leave of absence’, livelong ‘whole, entire’, of period of time, from Old English lēof ‘dear, beloved’, and libido, from Latin libīdō ‘pleasure, desire’.
[Pokorny *leubh-, pp. 683–684.]