In general, federal employee's have a statutory (legal) right to "individually or collectively" petition (lobby) Congress. The law that covers this right is 5 U.S.C. 7211.
Section 7211 of Title 5 of the Unites States Code says:
"The right of employees, individually or collectively, to petition Congress or a Member of Congress, or to furnish information to either House of Congress, or to a commit tee or Member thereof, may not be interfered with or denied."
Section 7211 of Title 5 of the Unites States Code
This right of federal employees to contact Members of Congress is undeniable to employees so long as they are not on duty time and not using government property or government resources.