You already got good answers, but I wanted to add that you might be mixing up ~ㄹ게요 with something else. You say 'ㄹ게요 is used when we talk about a prediction, a plan or even an unconfirmed "truth"'', but that sounds like a description for ~겠다 / ~겠어(요), an entirely different ending form even though both have '게' in them. ~겠다 might also look like the past tense of ~ㄹ게 but it is not - it's only used in the present tense, and any similarity is a pure coincidence. ~겠다 can mean those three things you mentioned. 1. 쟤 (저 아이) 넘어지겠다 - I'm afraid that boy might fall down (concern/prediction about what might happen). 2. 난 이곳을 떠나겠어 - I will leave this place (firm intention or plan - much more serious than ~ㄹ게). 3. 이것은 큰 이변이라 하겠다 - This may be a great unexpected turn. (factual statement - 하겠다, meaning 말할 수 있겠다, softens the tone and makes it less definite than 이다 would) ~ㄹ게 only has some overlap with the #2 sense above, but it is lighter and more casual than ~겠어.

ㄹ 게요 is correct. When we speak ㄹ게요 it sounds like ㄹ께요.