Purpose of L2,L3 & C6 in the following CW transmitter circuit
L2 has an impedance of over 300 ohms at 27 MHz so it's fairly certain that this is being used as an inductor that allows the AC signal on the transistor collector to be freely developed whilst passing a DC current to said transistor.
L3 is to base load the 12" (300 mm) antenna and make it resonant at 27 MHz. A normal quarter wave monopole antenna would be a quarter wave long and, at 27 MHz this would be nearly 3 metres so, L3 helps make the "short" monopole resonate at 27 MHz.
C6 is just to prevent DC voltages on T2's collector being shorted in case the antenna touched ground.


So, for a short monopole look at this diagram of impedance: -



There is a red dot that approximates to 12" (300 mm) and that tells us that a short monopole of this length will have a capacitive reactance of about 1800 ohms. In terms of actual capacitance this is about 3.3 pF i.e. the monopole will look like 3.3 pF. This is series resonated by the 10 uH (L3) at this frequency: -

\$f = \dfrac{1}{2\pi\sqrt{LC}}\$ = 27.7 MHz 

i.e. L3 is about the right ball-park for base-tuning a short monopole.