I’ve managed to include lemmy.ml and fapsi.be search results in my public searx instance on search.bka.li

To do the same, open the settings.yml file of your searx installation, search for the engines: part and add the following lines:

  - name : lemmy
    engine : json_engine
    search_url : https://lemmy.ml/api/v3/search?q={query}&page={pageno}&type_=Posts
    results_query : posts
    url_query : post/ap_id
    title_query : post/name
    content_query : post/body
    categories : general, social media
    shortcut : le
    paging : True
    disabled : False

After restart, you’re able to see and select lemmy at the searx preferences page under the tabs general and social media. A search would look like this:
Source: search.bka.li

You can also add comments:

  - name : lemmy comments
    engine : json_engine
    search_url : https://lemmy.ml/api/v3/search?q={query}&page={pageno}&type_=Comments
    results_query : comments
    url_query : post/ap_id
    title_query : post/name
    content_query : post/body
    categories : general, social media
    shortcut : lec
    paging : True
    disabled : False

As well as communities:

  - name : lemmy communities
    engine : json_engine
    search_url : https://lemmy.ml/api/v3/search?q={query}&page={pageno}&type_=Communities
    results_query : communities
    url_query : post/ap_id
    title_query : post/name
    content_query : post/body
    categories : general, social media
    shortcut : leco
    paging : True
    disabled : False

User search is possible too, but adding this would only support bullying and stalking. For ethical reasons, I decline to post an example of this as well.
Be careful: Never use the same shortcut for different engines. When your searx will not load or time out, check the shortcut first.