Can LMATRIX be used for an axisymmetric model? The documentation mentions that
it works with solid97 and solid117 solenoidal formulations.

Yes, LMATRIX can be used for 2d axisymmetric elements, such as PLANE53 as well.
I attached a qa test input (ev53-54s.dat) The command documentation you refer to
was added to confirm that the new "solenoidal" option for solid97 and solid117 is supported.

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