An old question without an answer; maybe you solved the problem
already. But as it is not closed yet I want to share my ideas.
The question is not very clear. As stated in the comments (1) the
answer may look at the output, i.e., you want to have LaTeX code
instead of TeX code as the result of the weave process, or you want
(2) to write LaTeX code instead of Pascal in WEB, or, as you mention
Lyx, you want (3) the status of your WEB coding, i.e., the output of
weave, appear as DVI or PDF output. (I assume you do not want to talk
about Lyx noweb class.)
(1) can be achieved with noweb; (2) can be done with noweb or with
spider; (3) is difficult because weave has not one but two input
files and needs no open ends; but you can do it.
About (1): As mentioned in the comments noweb has different backends
and you can make one to output LaTeX instead of TeX. But according to
your answer to the comment this seems not to be your
question/problem. Moreover, it does not make sense as no one looks at
the output of weave.
About (2): WEB is a TeX/Pascal combination and CWEB is a TeX/C
combination. The language is important as the corresponding weave
process has to format the code. For advocates of literate programming
this is an important point; see this
article of Bart
Childs. But on the other hand this approach leads to a lot of
different systems to support the paradigm of literate programming for
different programming languages. See the CACM
So if you want LaTeX as a programming language you first have to
define how LaTeX has to be formatted. TeX code is usually output
without special markup in typewriter fonts. This is ideal for noweb
but doesn't fulfill the criteria of the above cited article by Childs
for a useful tool. (This
article shows how to
deal with plain.tex.)
You can use
earlier system by the author of noweb (see the cited article by
Childs) to implement your format rules.
I use a noweb like style but have coded my own backend and output the
code as described above; see this
reduces the number of WEB commands but this comes with a price about
the fine control of the output.
About (3): This is a little bit difficult. The weave processor needs
two input files (.web and .ch) and it must find all section titles. So
if you use in your code the name of a chunk that hasn't been coded
yet, weave fails. That means, you need a different program that
outputs what is written as .web without checking for completeness; and
it has to deal with loose ends that are not cited yet. This is
possible (my first replacement for noweb's weave gives only warnings)
but I don't think such a tool has been made public.
If you start to code in a WEB like system you may not feel the need to
have incomplete output. The features of your editor are more
important, I think.