you have to differentiate the authorization to work on LSMW, which means administration of LSMW objects, creating new LSMW objects, changing existing objects, or just execution of LSMW, from the authority to post the data.
You can have users to create LSMW objects to change materials for example, but they will not succeed to change a material if they do not have the standard material master maintenance authority.
you also need to consider which authority you give for a development system and for a production system.
E.g. you do not need the authority to create LSMW in a production system, this is only needed in development, you only need the authority to execute an existing LSMW in production.
Outside a project nobody really needs the LSMW authority in production.
Please see the docu: Authorizations - Legacy System Migration Workbench - SAP Library