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Hi, I'm Mike G and I'll be assisting you. Are both lights at the end of the 300ft? What voltage? Are you going to have any receptacles for power?
For the length of the run and the loads(2 lights & 1 receptacle. I suggest installing a small 3R sub panel to allow for only a single feed circuit . multiple circuits which would be 3-20A for the loads and the wire size make it a better way to do it. Your thoughts.
60A sub panel 2-#4, 1-#6 & 1-#10 copper THWN. 1" conduit min but 1 1/4" suggested.
A pullbox at the shoreline.
Might be better to speak with you on the phone.