The most common and most likely answer to this crossword clue is the 10 letter word UNSCHOOLED
I've seen this crossword clue in The Times
U
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Buddy explains!

The straight part
We know that "Lacking formal education" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case lacking formal education = unschooled.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does UNSCHOOLED mean?
UNSCHOOLED adjective- Not schooled; not having been to school.
- Inexperienced; not having developed skill or knowledge in some area.
- To educate (a child) in an alternative to the regular school method, focused on the learner-chosen activities as a primary means for learning.