Thanks for your hint: I didn't know that subtelty about Lucida OT (and I don't know how to set it up when using Lucida OT).
That being said, actually what I would like to use is the kind of script font which is the attached document (those script fonts were widely used in higher mathematics textbooks in France).
So when I use mkiv the result is the one I like and is attached to this message (test-scriptfonts-mkiv.pdf). However, thanks to your message I went to check, and noticed that lmtx does not give the same math script fonts, and I don't know what has changed between mkiv and lmtx regarding Asana Math, or the way in which fallback fonts are managed (please see the attached file test-scriptfonts-lmtx.pdf).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Some Font Definitions
\definefallbackfamily[myfont][math][Asana Math]
[range={uppercasescript,lowercasescript}]
% lucida font
\definefontfamily[myfont][serif][Lucida Bright OT]
\definefontfamily[myfont][math][LucidaBrightMathOT]
\definefontfamily[myfont][sans][LucidaSansOT]
\definefontfamily[myfont][mono][LucidaSansTypewriterOT]
%\setupbodyfont[myfont,10pt]
%% End of Font Definitions
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\starttext
\startbuffer[test]
Testing script fonts in maths
\startformula
x^2 + y^2 = z^2, \quad \sin(a)^2 + \cos(b)^2 = 1.
\stopformula
\startformula
\cal{A},
\quad \cal{B},
\quad \cal{C},
\quad \cal{D},
\quad \cal{E},
\quad \cal{F},
\quad \cal{G},
\quad \cal{H},
\quad \cal{K},
\quad \cal{L},
\quad \cal{M},
\quad \cal{P},
\quad \cal{S},
\quad \cal{T}
\stopformula
\hairline
\stopbuffer
\switchtobodyfont[lucidaot]
{\bf Lucida OT: }
\getbuffer[test]
\switchtobodyfont[myfont]
{\bf Lucida OT with Asana Math: }
\getbuffer[test]
\stoptext