The most common and most likely answer to this crossword clue is the 8 letter word ALKALINE
I've seen this crossword clue in The Times
A
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More clues leading to the result ALKALINE
Buddy explains!

The straight part
We know that "Like lime perhaps" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case like lime perhaps = alkaline.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 ALKALINE mean?
ALKALINE noun- An alkaline battery.
- Of, or relating to an alkali, one of a class of caustic bases.
- Having a pH greater than 7.