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The following is from the README from the lame source:
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This code is distributed under the GNU LESSER PUBLIC LICENSE
(LGPL, see www.gnu.org) with the following modification:

1. If you determine that distribution of LAME requires a patent license,
   and you obtain a patent license, you may distribute LAME even though
   redistribution of LAME may also require a patent license.  

2. You agree not to enforce any patent claims for any aspect of
   MPEG audio compression, or any other techniques contained in 
   the LAME source code. 

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The following is from the LICENSE file from the lame source:
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Can I use LAME in my commercial program?  

Yes, you can, under the restrictions of the LGPL.  The easiest
way to do this is to:

1. Link to LAME as separate library (libmp3lame.a on unix or 
   lame_enc.dll on windows)

2. Fully acknowledge that you are using LAME, and give a link
   to our web site, www.mp3dev.org

3. If you make modifications to LAME, you *must* release these
   these modifications back to the LAME project, under the LGPL.


*** IMPORTANT NOTE ***

The decoding functions provided in LAME use the mpglib decoding engine which
is under the GPL.  They may not be used by any program not released under the
GPL unless you obtain such permission from the MPG123 project (www.mpg123.de).

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Running "lame --license" (or viewing frontend/parse.c) reports:
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LAME version 3.96.1 (http://lame.sourceforge.net/)

Can I use LAME in my commercial program?

Yes, you can, under the restrictions of the LGPL.  In particular, you
can include a compiled version of the LAME library (for example,
lame.dll) with a commercial program.  Some notable requirements of
the LGPL:

1. In your program, you cannot include any source code from LAME, with
   the exception of files whose only purpose is to describe the library
   interface (such as lame.h).

2. Any modifications of LAME must be released under the LGPL.
   The LAME project (www.mp3dev.org) would appreciate being
   notified of any modifications.

3. You must give prominent notice that your program is:
      A. using LAME (including version number)
      B. LAME is under the LGPL
      C. Provide a copy of the LGPL.  (the file COPYING contains the LGPL)
      D. Provide a copy of LAME source, or a pointer where the LAME
         source can be obtained (such as www.mp3dev.org)
   An example of prominent notice would be an "About the LAME encoding engine"
   button in some pull down menu within the executable of your program.

4. If you determine that distribution of LAME requires a patent license,
   you must obtain such license.


*** IMPORTANT NOTE ***

The decoding functions provided in LAME use the mpglib decoding engine which
is under the GPL.  They may not be used by any program not released under the
GPL unless you obtain such permission from the MPG123 project (www.mpg123.de).

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The mpglib/README file included with the lame source says:
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COPYING: you may use this source under GPL terms!

PLEASE NOTE: This software may contain patented algorithms (at least
  patented in some countries). It may be not allowed to sell/use products
  based on this source code in these countries. Check this out first!

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The libmp3lame/fft.c file from the source includes:
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** NOTE: This routine uses at least 2 patented algorithms, and may be
**       under the restrictions of a bunch of different organizations.
**       Although I wrote it completely myself; it is kind of a derivative
**       of a routine I once authored and released under the GPL, so it
**       may fall under the free software foundation's restrictions;
**       it was worked on as a Stanford Univ project, so they claim
**       some rights to it; it was further optimized at work here, so
**       I think this company claims parts of it.  The patents are
**       held by R. Bracewell (the FHT algorithm) and O. Buneman (the
**       trig generator), both at Stanford Univ.
**       If it were up to me, I'd say go do whatever you want with it;
**       but it would be polite to give credit to the following people
**       if you use this anywhere:
**           Euler     - probable inventor of the fourier transform.
**           Gauss     - probable inventor of the FFT.
**           Hartley   - probable inventor of the hartley transform.
**           Buneman   - for a really cool trig generator
**           Mayer(me) - for authoring this particular version and
**                       including all the optimizations in one package.
**       Thanks,
**       Ron Mayer; mayer@acuson.com

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Although lame_enc.dll is not included with the package, the
Dll/LameDLLInterface.htm webpage (included with the source) says:
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People and companies who wants to distribute
lame_enc.dll with their commercial products are free to do so as
far as I'm concerned (LGPL license), but should be aware that
lame_enc.dll might infringe certain MP3 related software patents
held by Fraunhofer IIS in certain countries.

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Also see
http://www.mp3licensing.com/help/developers.html#55
and section 11 in the LGPL and section 7 in the GPL.