I need to understand the use case. What's the purpose? what kind of block is that? LiteMage is designed to generate a full page from cache by combining public and private blocks. If there's a block that always has to hit Magento backend, that will slow down the whole site if every request has to go to backend. If you let me know more detail, there maybe better ways to address your issue.
To exclude one block from cache, you can add one block definition in config.xml esiblock section, add a line attribute <ttl>0</ttl>. We did not include this in our document, as I haven't encounter any real use case of it.
Lauren