SQL is really meant for server environments or environments that require persistent storage and quick lookups.
Mentioning 'servers' is off topic. MySQL is a multi-connection database that lives on a server but that's not what the OP is asking for. The OP would like SQLite which is queryable local storage for a single-connection (i.e. the player). SQLite is appropriate for many applications particularly for large datasets.
If the OP is looking for some sort of an MMO game, then he/she could use a server model that is written outside of LOVE that supports SQL and just send the data in a serialized form to the clients, decode it, and BAM.
Correct. A MMO game needs a serverside database. In this scenario there is hardly any client persistent data so SQLite would unlikely be needed. However, this is not what the OP asked for.
Not to mention one key thing in regards to SQL is that it is not going to halt your code until a result is returned...
There is a small delay when reading/writing to SQLite opposed to changing variables in memory but that delay isn't always a problem. Imagine a turn-based game for a space game with 10,000 planets each with 20 variables (i.e. 200000), the data can be manipulated during the player's thinking time, so the read/write time isn't ever observed. But crucially the game doesn't have to keep every variable in memory all the time. Also note the read/write time for parsing and saving large XML or JSON files would likely take longer (because it's writing to the filesystem opposed to a database) and more CPU (because it is a more intensive task). Note: If you don't think 200000 is large enough simply imagine a larger number
What I propose is support for it (in other words, simple modules as previously stated were already possible), but not there by default.
A module is workable but I think the problem is that cross platform deployment becomes more difficult / less convenient.
As mentioned by others, SQLite is very powerful and useful. XML, JSON and Lua tables all have their place but they don't replace SQLite's features. Gideros and CoronaSDK, Moai and even web browsers from 2010 (under the name WebSQL) all support SQLite. I come from relational database background so I have to disagree with the suggestion that parsing text files is an adequate substitute.
This thread has had over 2000 views in 5 weeks, so clearly there is some interest. My preference would be for it to be included like the other Lua engines. 2nd preference is for an install guide to be added to the wiki. And obviously there will be some bias here because many of you won't be using SQLite (partly because it's not mentioned in the wiki or available in API), that's not to say it's not useful.