easily – легко; easy – легкий, нетрудный; ease – облегчать, легкость, простота.

easily (adv.)
late 13c., aisieliche, from easy + -ly (2).
easy (adj.) (из старофранцузского «aisie» - удобный, легкий, богатый); причастие прошедшего времени от «aisier»
c.1200, "at ease," from Old French aisie "comfortable, at ease, rich, well-off" (Modern French aisé), past participle of aisier "to put at ease," from aise (see ease).

Sense of "not difficult to deal with" is mid-14c.; of conditions, "comfortable," late 14c. The concept of "not difficult" was expressed in Old English and early Middle English by eaþe (adv.), ieþe (adj.), apparently common West Germanic, but of disputed origin. Easy Street first printed 1901 in "Peck's Red-Headed Boy." Easy money attested by 1896; to take it easy "relax" is from 1867; easy does it recorded by 1891. Easy rider (1912) was U.S. black slang for "sexually satisfying lover." The easy listening radio format is from 1965, defined by William Safire (in 1986) as, "the music of the 60's played in the 80's with the style of the 40's." Related: Easier; easiest.

ease (n.) (из старофранцузского «aise» - удобство, удовольствие, возможность); происхождение неизвестно.
early 13c., from Old French aise "comfort, pleasure, well-being; opportunity," of unknown origin, despite attempts to link it to various Latin verbs.

The earliest senses in French appear to be 1. "elbow-room" (from an 11th century Hebrew-French glossary) and 2. "opportunity." This led Sophus Bugge to suggest an origin in Vulgar Latin asa, a shortened form of Latin ansa "handle," which could be used in the figurative sense of "opportunity, occasion," as well as being a possible synonym for "elbow," because Latin ansatus "furnished with handles" also was used to mean "having the arms akimbo." OED editors report this theory, and write, "This is not very satisfactory, but it does not appear that any equally plausible alternative has yet been proposed."

В очередной раз сказочки.

Английское «easily» и есть основное слово. И слово это – осилю. СЛ – SL – easily. Впрочем и французское "asier" - тоже самое, но с заменой "л" - "r".