You can contact your local honda parts dealer to find out if the dx/lx tranny is compatible with the ex motor vice versa.

More then likely they are crosscompatible like bseries & dseries trannys.

The only places I know that might have a 2k1-2k3 civic tranny are:
importautosalvage.com
ebay.com
or any local salvage yard like starkey autosalvage etc.

or if you have too, new from honda.... ouch