The Solvent of choice for gluing or repairing Polycarbonate (Lexan) is Methylene Cloride, next best Methyl Trichloride (Chloroform). Methylene Cloride will dissolve lexan without crazing it.
Be wary of some of the commercial solvents like Plexisolv or Plastruct because some of these contain Glacial acetic acid and I am not sure what that does to Lexan.
The Methylene Cloride can be made into a soup by dissolving chips of Lexan into it.
Two part glues like weld-on 45 are good, however. they are amber in color and will not give you an invisible join. I hope this is of help.
Brian Evans.