If Lionel is using plastic for these steps it may be Delrin or a similar plastic. Stryene would break way too easily. If it is Delrin solvent cement won't work. Put a drop on it to make sure. If its Delrin the solvent will just evaporate off without melting the plastic.
In that case CA, super glue, is likely the best choice. Contact cement like Goo or Plyobond will work too.
Pete