It is the third one, 걸려요. Tow back-to-back ㄹs make an L-like sound, like /geolyeoyo/ ( /eo/ standing for the Korean ㅓ). So you can pronounce the two ㄹs like a single L. There shouldn't be additional syllable or lengthening of a syllable.
거려요 is /georyeoyo/. So the difference between 걸려요 and 거려요 is just L vs R.
걸-여-요 you wrote is impossible to pronounce at the speed of speech. 걸여 becomes 거려 because we smoothly connect the syllables. The only way to pronounce 걸여 as 걸 and 여 is to insert a substantial pause between the two syllables which would make it very unnatural.
The following examples illustrate the double ㄹ as L and single ㄹ as R principle.
* green -> 그린. glean -> 글린.
* brew -> 브루, blue -> 블루.
Before a consonant or at the end of a phrase, L-like sound is represented by double ㄹas usual whereas R is spelled as single ㄹ or sometimes simply dropped.
* cult -> 컬트, curt -> 커트. (weak R is usually dropped, kind of like British English does. If you must include the R sound, you can make it 커르트)
* Portugal -> 포르투갈, Poland -> 폴란드.
* palace -> 팰리스, Paris -> 파리 (or 빠리 as some people pronounce it)