Hi,
Lightstreamer does not keep the snapshot while no client is subscribed. In your server log you should see the "Unexpected update" message(s) when you issue an update and there are no clients.
Your adapter should be able to retrieve and send the snapshot when the subscribe method is called (that is the first client is connected). After that the server will handle the snapshot for other clients subscribing to the same item.
Another, less reliable, option is to keep a fake client always subscribed to your item. You might code it directly into your adapter.
In any case please take a look to the General Concepts file (section 4), it will probably clear things up for you:
http://www.lightstreamer.com/latest/Lightstreamer_Allegro-Presto-Vivace_5_1_Colosseo/Lightstreamer/DOCS-SDKs/General%20Concepts.pdf