Regardless of the true etymology of "obliegen" it is patently the case that the various meanings of the verb "to oblige"
1: to constrain by physical, moral, or legal force or by the exigencies of circumstance
2 a: to put in one's debt by a favour or service
b: to do a favour for
together with the entry in http://dictionary.reference.com/browse/oblige
verb, o·bliged, o·blig·ing.
–verb (used with object)
1. to require or constrain, as by law, command, conscience, or force of necessity.
2. to bind morally or legally, as by a promise or contract.
3. to place under a debt of gratitude for some benefit, favor, or service: I'm much obliged for the ride.
4. to put (one) in a debt of gratitude, as by a favor or accommodation: Mr. Weems will oblige us with a song.
5. to make (an action, policy, etc.) necessary or obligatory: Your carelessness obliges firmness on my part.
–verb (used without object)
6. to be kindly accommodating: I'll do anything within reason to oblige.
include the sense of the existing LEO entry "to be incumbent (on|upon) so.", and and "to oblige" should accordingly be added as a valid translation of "obliegen". Note also that "obligation" is already listed in LEO as a translation of "Obliegenheit"