I finally solve this problem by inserting the LaTeX code at the beginning
of the document ( not in the preamble):
\renewcommand{\remarkname}{備註}
\renewcommand{\casename}{案例}
\renewcommand{\theoremname}{定理}

This work around is inspired by this page:
https://tex.stackexchange.com/questions/24878/cjk-package-and-figurename
It says that any cjk character should be put in the cjk environment, but
the cjk environment can be placed only in the body rather than the preamble.

Originally, in the Source Pane, I see the commands in the preamble:
\providecommand{\remarkname}{備註}
\providecommand{\casename}{案例}
\providecommand{\theoremname}{定理}
I guess it's probably why it's not dealt with by the cjk package.

On Sat, Sep 8, 2018, 11:48 Erik Apostol (Che-hsiu Cheng) <
erikapos...@gmail.com> wrote:

> I'm using LyX 2.2.3, and I found that theorem names, such as theorem,
> case, remark, in Chinese are not shown correctly. For example, I have a
> .lyx file with content
>
>> 定理 1. 一二三四五
>> 案例 1. 六七八九十
>>
>>
>> 備註 2. 十一時二十三
>>
> in which 定理 is the Theorem environment, 案例 is the Case environment, and 備註
> is the Remark environment. But after export to pdf (via pdflatex) it's
> shown as
>
>> åőŽçŘĘ 1. 一二三四五
>> æąĹä¿Ń 1. 六七八九十
>> åĆŹèĺż 2. 十一時二十三
>>
> Only theorem names are garbled, but other Chinese words are normal.  In
> Document settings, I've set CJK font to *bsmi*, language to *Chinese
> (traditional)*, and encoding to *Unicode (CJK) (utf8)*. The original LyX
> file is here
> <https://www.dropbox.com/s/ilvjvc6m380i55f/Abnormality%20of%20Chinese.lyx?dl=0>
> .
>
>

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