There is no datasource for SQLite in Grafana. I am testing a MySQL database in parallel with InfluxDB which is working very well if you don't want to use InfluxDB, which is probably the best choice for time series.
InfluxDB is not only better integrated to Graphana but is also much better suited to capturing and processing time series data.
Handles timestamped data natively
Allows summary/aggregated data to be calculated & saved automatically - for example, I keep my detailed sensor data (at ~1 minute intervals) for 7 days but all the data is automatically aggregated to hourly data (avg, max & min) and kept indefinitely. InfluxDB does all of this itself.
Native integration to Graphana.
The disadvantage is that you have to learn something that you will initially find a little more complex than standard SQL to begin with.
I have influxdb and grafana running on a Raspberry Pi3 and they're well suited. I rarely use more than 3% cpu power and grafana is very quick to upload and display a months worth of data.
Both are now available from the repository which makes them ultra easy to install.
I've used both MySQL and SQLite and both are excellent but influxdb is not only ultra easy to install and very little setup required.
+1 for influxdb & grafana
PS: if you are used to relational database time series dbs are a different animal and will require a little learning curve.