A bit of technique first. LyX is based on Qt, and Qt delegates the input of Unicode character to input to a component called the Input Method. This includes typing the code point directly, as stated here: https://bugreports.qt.io/browse/QTBUG-8. Thus LyX receives the Unicode character directly in interpreted form from the Input Method. In particular what applies to other applications applies to LyX.
For instance, on Linux there is the input method IBus-LaTeX that lets one enter Unicode symbols in the LyX window (including mathematical symbols that LyX itself does not know) by entering its name in LaTeX (or XeTeX), which some may find more convenient than learning the code points. But the following page shows a similar software for entering the character with
Ctrl+Shift+U followed by the code point (Linux still): https://wiki.lyx.org/Tips/UnicodeInputUsingCtrl-Shift-U.
Knowing this, it is easy to find information about what the solution could be on Windows: http://www.fileformat.info/tip/microsoft/enter_unicode.htm. This page suggests several methods, the most likely to succeed being:
Alt, then press
+ (numerical keyboard), then type the hexadecimal code, and release
Alt. This may require editing the regisry and setting
EnableHexNumpad to "1" under
HKEY_Current_User/Control Panel/Input Method (with type
Use the Unicode Input Method Editor. It is enabled by setting a language such as
Chinese - Unicode in the Regional Settings, and it triggers with the key
LeftAlt Shift followed by the hexadecimal code.
If none of the methods above work, it might be a sufficient reason to fill in a bug report at http://www.lyx.org/trac/wiki/BugTrackerHome.
Finally, LyX converts the Unicode code points into commands understood by LaTeX. But since LaTeX does not handle many different characters, LyX could warn that certain characters are unencodable in LaTeX. One must then switch to XeTeX or LuaTeX by checking “Use non-TeX fonts” in the document preferences.
That being written, for the use that you suggest, you are probably better off defining a Math Macro once and for all and type it by its custom LaTeX command name directly in LyX's math mode.