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LanguageToolCheck and LanguageToolClean are 2 commands used in vim-languageTool plugin.
LanguageToolCheck command check and list out spelling errors of your text. And LanguageToolClear will clean the error list. During error checking mode. User then can use :lne to jump to the next error. I wonder how to map the n to :lne command when LanguageToolCheck command is executed and map back to normal function (jump to next highlighted) for n when LanguageToolClear is executed
This is not exactly what you asked for, but well known plugin vim-unimpaired by Tim Pope adds short mappings for many commands, including :lnext which is the one you're after.
The vim-unimpaired mappings generally use [ and ] as its direction ("previous" vs "next", or "on" vs "off") followed by a single letter to identify the object (l for the location list.)
So you have ]l for :lnext.
]l is not as short as just using n, but it might be something for you to consider, since it doesn't involve changing the behavior of n during an operation (it's quite possible you'll end up wanting to search in between LanguageToolCheck and LanguageToolClear.) You may also find the other mappings from vim-unimpaired to be quite useful, it's definitely among the plug-ins I tend to recommend.
coc-diagonostic-next if using the vim-coc, search the next spelling error when using LanguageToolCheck and search for the next highlight if highlight set is true. I would like to getting to know vim better and write a plugin for that