In case the mayor and council of any city of the third class shall have heretofore levied or shall hereafter levy any special assessment for any public improvement in said city, which special assessments are or may be informal, illegal, irregular or void for the want of sufficient authority to make or levy the same, or for any cause whatsoever, the mayor and council of such city may at any time relevy any such special assessments in the manner provided and against the property liable for assessment for such improvement at the time of the making thereof: Provided, That in all cases where informal, illegal, irregular or void special assessments levied for any improvement against any lot or piece of land shall have been paid, in whole or in part, such lot or piece of land shall not be reassessed for the assessment or the part thereof so paid.