SOURCE

let selectLessonList=[
    {
        "child_id":5581,
        "school":6,
        "weeks":[
            {
                "week_id":110,
                "lesson_id":10
            }
        ]
    },
    {
        "child_id":5582,
        "school":6,
        "weeks":[
            {
                "week_id":110,
                "lesson_id":10
            }
        ]
    },
    {
        "child_id":5581,
        "school":43,
        "weeks":[
            {
                "week_id":125,
                "lesson_id":10
            }
        ]
    },
    {
        "child_id":5582,
        "school":43,
        "weeks":[
            {
                "week_id":125,
                "lesson_id":10
            }
        ]
    },
    {
        "child_id":5581,
        "school":6,
        "weeks":[
            {
                "week_id":118,
                "lesson_id":11
            }
        ]
    },
    {
        "child_id":5580,
        "school":6,
        "weeks":[
            {
                "week_id":110,
                "lesson_id":10
            }
        ]
    }
]
let childList=[{"child_id":5580,},{"child_id":5581,},{"child_id":5582,},]
let arr=selectLessonList
selectLessonList.map((item,index) =>{
        selectLessonList.map((childItem,childIndex)=>{
            if(item.child_id==childItem.child_id && item.school==item.school && index!=childIndex){
                if(selectLessonList[index].weeks.find(item=>item=selectLessonList[childIndex].weeks[0])){
                    selectLessonList.splice(childIndex,1)
                }else{
                    selectLessonList[index].weeks.push(...arr[childIndex].weeks)
                    selectLessonList.splice(childIndex,1)
                }
            }
        })
    })
console.log(selectLessonList)