LyX shouldn't be using Inkscape's Python and Inkscape shouldn't be using LyX's Python.
What's your PATH? Inkscape's directory shouldn't be in it, and I can't comment about LyX.
I'm trying to work out what the problem is, though; it's not very clearly worded. Is the problem occurring when using LyX or Inkscape? If it's LyX, the issue is with them, it is entirely their fault. They should be using their own location first, whatever.
LyX shouldn't be using Inkscape's Python and Inkscape shouldn't be using LyX's Python.
What's your PATH? Inkscape's directory shouldn't be in it, and I can't comment about LyX.
I'm trying to work out what the problem is, though; it's not very clearly worded. Is the problem occurring when using LyX or Inkscape? If it's LyX, the issue is with them, it is entirely their fault. They should be using their own location first, whatever.