map/filter

var upper = _.mapObject(obj, function (value, key) {
    return value.toUpperCase();
});

every / some

var r1 = _.every(obj, function (value, key) {
    return key === key.toLowerCase() && value === value.toLowerCase();
});

var r2 = _.some(obj, function (value, key) {
    return key !== key.toUpperCase() && value !== value.toUpperCase();
});