-(으)ㄹ래요
eul-lae-yo
The hand that picks one up: -(으)ㄹ래요
The picture Your own hand picking up one of the several things laid out in front of you. -(으)ㄹ래요 is what your own mind picked; -(으)ㄹ게요 is a promise handed to someone else.
Where the picture shows up in -(으)ㄹ래요
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what I picked off the menu
저는 냉면 먹을래요.
jeo-neun naeng-myeon meo-geul-lae-yo
I'll have the cold noodles.
A finger coming down on one line among the pages of a spread-open menu
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holding it out for them to choose
이거 한번 입어 볼래요?
i-geo han-beon i-beo bol-lae-yo
Do you want to try this on?
Lifting the garment toward them, passing the choice into their hands
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picking the option of not doing it
오늘은 집에 있을래요.
o-neu-reun ji-be i-sseul-lae-yo
I'd rather stay home today.
Between the front door and the living-room sofa, your body turning toward the sofa
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a hand held out to come along
같이 가실래요?
ga-chi ga-sil-lae-yo
Would you like to come with me?
The door left half open, the space beside you kept clear for them
To a senior, -(으)ㄹ래요? can sound a bit light. -(으)시겠어요? is more polite.
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leaving first, by my own will
저 먼저 갈래요.
jeo meon-jeo gal-lae-yo
I'm going to head off first.
Everyone else still seated while you pick up your bag and stand
All of it in one picture
-(으)ㄹ래요 is the motion of a hand picking one thing. Pick off the menu and it is an order; hold it out toward the other person and it becomes 'you choose'; turn toward the sofa and it becomes a refusal. Leave the door half open and it is an invitation; pick up your bag and it says you are leaving first. It is not a promise stamp — it simply shows the side your own mind has chosen.