Yes! Non-profit Organizations Can Lobby!
The Alliance for Justice, a non-profit organization, provides information on this issues as well as free technical assistance to non-profit organizations.
The Center for Lobbying in the Public Interest also provides information and free technical assistance to non-profit organizations.
Non-profit organizations have a lot to gain by advocating for change through the legislative process. The publication Worry Free Lobbying for Non-profit Organizations, provides information on the state and federal regulations that apply to non-profit organizations.
NP Action, a project of OMB Watch, is a great resource for information on non-profit lobbying.
OMB Watch is a watch dog organization whose issues include the federal budget, information and access, nonprofit advocacy, and regulatory policy.
The Independent Sector's publication, The Nonprofit Lobbying Guide
is an excellent guide for anyone wanting to know how to lobby.