The most common and most likely answer to this crossword clue is the 6 letter word LIFERS
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More clues leading to the result LIFERS
Buddy explains!

The straight part
We know that "Lags inside facing endlessly rigorous sentences initially" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case lags inside facing endlessly rigorous sentences initially = lifers.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 LIFERS mean?
LIFERS noun- A prisoner sentenced to life in prison.
- A prisoner sentenced to transportation for life.
- A person with a singular career path, especially in the military.
- A bird species seen for the first time by a birder who is keeping a list of all the species he or she has ever seen.