Dear Mr. Scott,
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We searched the National Archives Catalog and located the series Letters Received and Related Records Concerning Washington Territory, 1854 - 1890 and the series Transcripts of Executive Proceedings and Related Correspondence of the Governor of Washington Territory, 3/28/1877 - 1889 in the Records of the Office of the Secretary of the Interior (Record Group 48), that may include the correspondence that you seek. For access to these records, please contact the National Archives at College Park - Textual Reference (RDT2) via email at email@example.com.
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We were unable to locate any correspondence between Sheriff Packwood and Lester, however we did locate a Sheriff S.T. Packwood letter to Washington Territory Governor Eugene Semple regarding unrest among miners in Roslyn, August 23, 1888 among the Eugene Semple papers in the custody of the University of Washington Libraries Special Collections. We suggest that you contact them for a further search of their holdings.
We hope this is helpful. Best of luck with your research!