Since we don't know when Lua will get around to garbage collecting our userdata, we can't make any assumptions about the lifetimes of any references in the userdata.
Normally, Rust types passed to Lua must be Send, because Lua itself is Send, and must be 'static, because there is no way to tell when Lua might garbage collect them. There is, however, a limited way to lift both of these restrictions. You can call Lua::scope to create userdata types that do not have to be Send, and callback types that do not have to be Send OR 'static. However, after scope returns any UserData passed to Lua are invalidated (access from Lua will error).
The Lua API in general doesn't give out references to Lua values - you can only interact with them indirectly throught the API. In rlua, types like rlua::Table internally store an index into the current Lua stack, which is why they are only valid within the context callback.
There are some options for keeping longer references:
The Lua registry is a global Table available for use through the API. Add references using Context::create_registry_value() which returns a key which can be later used with Context::registry_value(), or provide your own key with Context::set_named_registry_value()/Context::named_registry_value().
A Lua value can be attached with a UserData value using AnyUserData::set_user_value()/AnyUserData::get_user_value(). With Lua 5.4+ multiple values can be stored using AnyUserData::set_i_user_value()/AnyUserData::get_i_user_value().