Ok so I have the game Clash of Clans. My Research Laboratory is level 3. How many times can I upgrade my lightning spell before it asks me to upgrade my research to level 4?
The maximum level you can obtain in Research Lab Level 3 is level 4(for your lightning spell). If you want your Lightning spell to be leveled up to level 5, you must upgrade your Research Lab to level 4.
As BiscuitBaker stated, the highest level you can get on Lightning spell is level 6(at least for right now).
At Lab level 3, the maximum level you can research for Lightning is 4.
Overall, the maximum level for the Lightning spell (currently, at least) is 6:
Though you'll need the eighth level lab (requires Town Hall 10) to get that far.