Adding genres and themes from work
I don't have a tool here to count, so I don't know how the numbers will
play out.  That said, I agree with the interpretation since there's a
lot of things going on here and it makes sense to detangle the function
into smaller bits.

The big if block immediately suggests that some kind of
short-circuiting or decomposing into functions would be useful.  E.g. if
workInfo is not an object, call persistWOrkDetails and just return;
the other branch will continue afterwards and also persists the object.

Then again, I'd rather split a function off in this case, though I have
no idea what to call it.

function addGenresAndThemesFromWork(work) {
    let workDetails = {workId: work.$.id, genres: [], themes: []};

    if (typeof work.info === 'object') {
        fillInWorkDetails(work.info, workDetails);
    }

    if (!_.has(workDetails, 'picture')) {
        workDetails.picture = {src: '/default.jpg', temporary: true};
    }

    persistWorkDetails(workDetails);
}


Next up are the genres and themes, which exhibit a common pattern, so
again, move that into a separate function.  Sounds like that is a
function that might already exist in a library anyway.

function pushNew(thing, name) {
    let value = {name: name};

    if (thing.findOne(value) === undefined) {
        thing.insert({name: name});
    }
}

...

case 'genres':
    workDetails.genres.push(workInfoValue);
    pushNew(Genres, workInfoValue);
    break;
case 'themes':
    workDetails.themes.push(workInfoValue);
    pushNew(Themes, workInfoValue.toLowerCase());
    break;


For "objectionable content" (I wonder) the if can be replaced with an
or, that is:

workDetails.mature = workDetails.mature || workInfoValue.toLowerCase() === 'ma';


The syntax is a bit longer, but a temporary variable could be used to
deal with that.


Is there a particular reason to use Object.keys instead of for
... in on the workInfo object?
The nested else { if ... } can just be written as else if in this
case.
workInfo[key] appears way too often, just assign it to a shorter
name.
Since you create workDetails yourself, you probably don't have to
use _.has, but just plain in.
The picture default value can be moved into the workDetails
initialisation since the loop will always overwrite the existing
value.  That also takes care of any possible issues with undefined.
If a function (like findOne) only returns a false value if couldn't
find something, then the comparison can also simply be if
(!findOne(...)) - I'm assuming that that's done for a reason though.


With all that in mind I'm arriving at the following, which, depending on
the exact format and semantics of the objects could be further
distilled, but I think this is good enough for now and for you to
continue on it later.

I'd also suggest that the workDetails object is filled in with more
defaults so it's actually clear that e.g. a missing mature field
actually means the same as mature: false in the initialisation (or
not, in which case the code below is slightly wrong).

function pushNew(thing, name) {
    let value = {name: name};

    if (thing.findOne(value) === undefined) {
        thing.insert(value);
    }
}

function pictureValue(img) {
    if (img[1] !== undefined) {
        return img[1].$;
    } else if (img[0] !== undefined) {
        return img[0].$;
    }
    return undefined;
}

function fillInWorkDetails(workInfo, workDetails) {
    for (let key in workInfo) {
        let value = workInfo[key];
        let workInfoValue = workInfo[key]._;

        switch (value.$.type.toLowerCase()) {
            case 'genres':
                workDetails.genres.push(workInfoValue);
                pushNew(Genres, workInfoValue);
                break;
            case 'themes':
                workDetails.themes.push(workInfoValue);
                pushNew(Themes, workInfoValue.toLowerCase());
                break;
            case 'main title':
                workDetails.name = workInfoValue;
                break;
            case 'plot summary':
                workDetails.plot = workInfoValue;
                break;
            case 'objectionable content':
                workDetails.mature = workDetails.mature || workInfoValue.toLowerCase() === 'ma';
                break;
            case 'picture':
                workDetails.picture = pictureValue(value.img) || workDetails.picture;
                break;
            case 'alternative title':
                if (value.$.lang.toLowerCase() === 'ja') {
                    workDetails.alternativeTitle = workInfoValue;
                }
                break;
        }
    }

    return workDetails;
}

function addGenresAndThemesFromWork(work) {
    let workDetails = {
        workId: work.$.id,
        genres: [],
        themes: [],
        picture: {src: '/default.jpg', temporary: true}
    };

    if (typeof work.info === 'object') {
        fillInWorkDetails(work.info, workDetails);
    }

    persistWorkDetails(workDetails);
}