Is there a reason that he used a slight excess?
Probably to compensate for any side reactions, water content the other reagents used, atmospheric moisture etc.
Why did he use so much diethylamine?
Because it's dirt cheap compared to lysergic acid, and he wanted to make sure that all all the latter molecules would get a chance to react. Some of the diethylamine will also be tied up as relatively unreactive salts with H2PO2Cl2 and other oxyacids formed by the reaction of POCl3 with water and lysergic acid. Some might even form phosphorous diethylamides with the POCl3 directly, but I'm not sure.