To set a Binary property just pass in a BinArray as the value and the Managed API will handle the rest. The value side of PidLidPropertyDefinitionStream is non-trival and you need to either copy an existing static value you know will always be the same or build your own code to construct the stream. (The stream itself contain underlying mapi properties of varying types).
Byte[] StreamValue;
var PidLidPropertyDefinitionStream = new ExtendedPropertyDefinition(
DefaultExtendedPropertySet.Common,
0x8540,
MapiPropertyType.Binary);
appointment.SetExtendedProperty(PidLidPropertyDefinitionStream, StreamValue);