Here is an alternative solution. Let's start with a version that doesn't break across pages. We'll fix that later.
First, let's try to get the basic layout without the frames. Unlike the other solutions, I don't move the theorem head to the right, rather I move the theorem body to the left.
\defineenumeration[THEOREMenumeration]
[
text=Theorem ,%Space after Theorem is delibrate
title=yes,
alternative=hanging,
titlestyle=boldslanted, % or bolditalic
style=slanted, % or italic
width=fit,
]
\define\starttheorem
{\dosingleargument\dostarttheorem}
\def\dostarttheorem[#1]%
{\startTHEOREMenumeration[#1]%
\crlf
}
\define\stoptheorem
{\stopTHEOREMenumeration
}
\starttext
\input ward
\starttheorem[title={Riemann-Lebesgue}]
\input ward
Pour tout $f \in L^1({\Bbb T})$, on a
\startformula
\lim_{|n| \to ∞} c_n(f) = 0
\stopformula
\stoptheorem
\input knuth
\stoptext
which gives:

Now all we need is the frame. To get the bottom rule around the theorem head, you can use:
\defineenumeration[THEOREMenumeration]
[
....
headcommand=\THEOREMframed,
]
where \THEOREMframed is defined as:
\defineframed [THEOREMframed]
[
frame=off,
bottomframe=on,
location=low,
rulethickness=2bp,
]
which gives:

The rule overlaps with the next line, but we'll fix this later.
Now, to get the frame around the theorem body, change the definitions of \starttheorem and \stoptheorem to:
\def\dostarttheorem[#1]%
{\startTHEOREMenumeration[#1]%
\startTHEOREMframedtext
}
\define\stoptheorem
{\stopTHEOREMframedtext
\stopTHEOREMenumeration
}
where THEOREMframedtext is defined as:
\defineframedtext [THEOREMframedtext]
[
offset=0pt,
loffset=1em,
boffset=1em,
corner=15,
width=broad,
rulethickness=2bp,
before=,
after=,
strut=no,
]
which gives:

Note that the theorem is now too broad. We can fix that by using:
\defineframedtext [THEOREMframedtext]
[
....
width=\dimexpr(\hsize-\framedparameter{loffset} -\framedparameter{rulethickness})\relax,
....
]
Here is the complete code:
\defineenumeration[THEOREMenumeration]
[
text=Theorem ,%Space after Theorem is delibrate
title=yes,
alternative=hanging,
titlestyle=boldslanted, % or bolditalic
style=slanted, % or italic
width=fit,
headcommand=\THEOREMframed,
]
\defineframed [THEOREMframed]
[
frame=off,
bottomframe=on,
location=low,
rulethickness=2bp,
]
\defineframedtext [THEOREMframedtext]
[
offset=0pt,
loffset=1em,
boffset=1em,
corner=15,
width=\dimexpr(\hsize-\framedparameter{loffset} -\framedparameter{rulethickness})\relax,
rulethickness=2bp,
before=,
after=,
strut=no,
]
\define\starttheorem
{\dosingleargument\dostarttheorem}
\def\dostarttheorem[#1]%
{\startTHEOREMenumeration[#1]%
\startTHEOREMframedtext
}
\define\stoptheorem
{\stopTHEOREMframedtext
\stopTHEOREMenumeration
}
\starttext
\input ward
\starttheorem[title={Riemann-Lebesgue}]
\input ward
Pour tout $f \in L^1({\Bbb T})$, on a
\startformula
\lim_{|n| \to ∞} c_n(f) = 0
\stopformula
\stoptheorem
\input knuth
\stoptext
Now, to make sure that the body can split across the page, we need to change the framedtext with a textbackground. The keys of textbackgroud are different from that of framedtext. We start with:
\definetextbackground [THEOREMframedtext]
[
mp=ellframe,
location=paragraph,
leftoffset=1em,
topoffset=1.5ex,
bottomoffset=1em,
rightoffset=0pt,
rulethickness=2bp,
framecolor=black,
before=,
after=,
strut=no,
]

Now all we need to do is define the metapost graphic ellframe that draws the L-shaped frame. Before we do that, we need to decide what happens when the theorem overflows a page: should we draw L-shaped frames on both pages, or should we draw a straight line on the first page and an L-shaped frame on the second? What happens in the unlikely scenario that the theorem spans three pages? ConTeXt makes it easy to write code specialized to each scenario.
\startuseMPgraphic{ellframe}
begingroup;
interim linecap := butt ;
for i=1 upto nofmultipars :
if multikind[i] = "single" :
draw ( ulcorner multipars[i] --
( llcorner multipars[i] + (0, boxlineradius )){down} ..
{right}(llcorner multipars[i] + (boxlineradius, 0) ) --
lrcorner multipars[i] )
elseif multikind[i] = "first" :
draw leftboundary multipars[i]
elseif multikind[i]= "middle" :
draw leftboundary multipars[i]
elseif multikind[i]= "last" :
draw ( ulcorner multipars[i] --
( llcorner multipars[i] + (0, boxlineradius )){down} ..
{right}(llcorner multipars[i] + (boxlineradius, 0) ) --
lrcorner multipars[i] )
fi
boxlineoptions withpen pencircle scaled boxlinewidth ;
endfor ;
endgroup;
\stopuseMPgraphic
This is the output when there is no page break:

And this is the output when the theorem breaks across pages:

Here is the final complete code:
\defineenumeration[THEOREMenumeration]
[
text=Theorem ,%Space after Theorem is delibrate
title=yes,
alternative=hanging,
titlestyle=boldslanted, % or bolditalic
style=slanted, % or italic
width=fit,
headcommand=\THEOREMframed,
]
\defineframed [THEOREMframed]
[
frame=off,
bottomframe=on,
location=low,
rulethickness=2bp,
]
\definetextbackground [THEOREMframedtext]
[
mp=ellframe,
location=paragraph,
leftoffset=1em,
topoffset=1.5ex,
bottomoffset=1em,
rightoffset=0pt,
rulethickness=2bp,
framecolor=black,
before=,
after=,
strut=no,
]
\startuseMPgraphic{ellframe}
begingroup;
interim linecap := butt ;
for i=1 upto nofmultipars :
if multikind[i] = "single" :
draw ( ulcorner multipars[i] --
( llcorner multipars[i] + (0, boxlineradius )){down} ..
{right}(llcorner multipars[i] + (boxlineradius, 0) ) --
lrcorner multipars[i] )
elseif multikind[i] = "first" :
draw leftboundary multipars[i]
elseif multikind[i]= "middle" :
draw leftboundary multipars[i]
elseif multikind[i]= "last" :
draw ( ulcorner multipars[i] --
( llcorner multipars[i] + (0, boxlineradius )){down} ..
{right}(llcorner multipars[i] + (boxlineradius, 0) ) --
lrcorner multipars[i] )
fi
boxlineoptions withpen pencircle scaled boxlinewidth ;
endfor ;
endgroup;
\stopuseMPgraphic
\define\starttheorem
{\dosingleargument\dostarttheorem}
\def\dostarttheorem[#1]%
{\startTHEOREMenumeration[#1]%
\page[no]
\startTHEOREMframedtext
}
\define\stoptheorem
{\stopTHEOREMframedtext
\stopTHEOREMenumeration
}