LGPL predates the classpath exception by quite a while, and doesn't serve the same purpose at all.
The classpath exception is intended to cause the target software to not have a license change just because it used a certain runtime library (classpath).
The LGPL has different aims entirely (around allowing library components for software).
Essentially, the classpath exception was written for programming language runtime libraries (and is thus the basis of what later became the gcc runtime library exception).
The LGPL was written for random library software, and started out much earlier than the classpath exception (by a decade or two).
The classpath exception is intended to cause the target software to not have a license change just because it used a certain runtime library (classpath).
The LGPL has different aims entirely (around allowing library components for software).
Essentially, the classpath exception was written for programming language runtime libraries (and is thus the basis of what later became the gcc runtime library exception).
The LGPL was written for random library software, and started out much earlier than the classpath exception (by a decade or two).