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Thank you for contacting the History Hub!
The majority of military databases will only include a middle initial. Additionally, many servicemen in this time frame did not list their middle names upon enlistment. You may be able to request a copy of his Official Military Personnel File (OMPF) from the National Archives in St. Louis. This record series consists of Navy servicemen retired or discharged between 1886 and 1994. The files contain basic biographical information as well as military training and bases where they served. Often times they also include identification pictures and personal correspondence. There is no comprehensive list of these files we can use to answer your specific question via History Hub.
These records are releasable to the public when the date of separation becomes 62 years from today’s date. You may request these OMPFs to view in our Research Room for no charge or complete an SF-180 form and send it to the following address:
National Archives and Records Administration
National Archives at St. Louis
PO Box 38757
St. Louis, MO 63138
Since there are most likely more than one Lester F. Harpers, do not include this service number on your request.