I agree with both two answers. BTW, in electrical point of view, IGBT/MOSFET power switches which is used in commercial grid-connected inverter can be classified as voltage source/sinks. The AC grid side is also a voltage sink. In the definition of two port electrical component, if the input is the voltage, the output must be the current, and vice-versa. This means you cannot directly connect a voltage source to a voltage sink. In this case that means a direct connection between IGBT switches and grid confronts basic physical law.
So it become easy to explain the role of inductor, or LCL circuit in your question.
in case of L filter, switches generates an input (voltage) for the inductor, so the output of the inductor L is current. Then the output of L which is actually current fed into grid, is the input of grid, and the output of grid, as you knew, is the constant AC voltage (110V@US, 230V@Europe).
In case of LCL filter, switches generates an input (voltage) for the inductor L1, so the output of the inductor L1 is current. Then the output of L1 is actually current fed into the capacitor C. The output quantity of C is the voltage which is the input of the inductor L2. Then the output quantity of L2 is currrent again and is fed into grid.
By applying the same explanation, you will able to explain why they NEVER put an LC/ or RLC (low-pass filter) between power switches of converters and grid.
If you want to optimize your design regarding to L /LCL filter, I propose to read this paper: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6872538 , which was studied by Prof. Solero and his colleagues at Roma Treo University.