in which rules are hachu different from lishogi?

Hachu rules
1. Baring the king is not a win condition.
2. 香車 cannot promote on the 12th rank on a non-capture, if it previously declined promotion.
3. If a 獅子 is only defended once by 歩 or 仲人, you can capture both with your 獅子 in one move.

so the first two are easy to solve, the third one, hmm why lishogi doesn't follow hachu rules?

Because HaChu rules conflict with JCSA rules.
In JCSA rules, Lion trading of the Lion protected by sole pawn or GB defender, is illegal

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