Ok. This should do it.
U1b/R2/C3 form a ~23kHz oscillator whose output is integrated by R3/C4 to give an approximation of a triangle wave. When the switch is closed C5 charges via the pot to generate a rising voltage ramp. The wave and ramp are summed, at the input of U1c, by R5/R6, to give a PWM output which switches Q1 and Q2 to drive NMOS FET M1 and hence the load (your string of LEDs plus current-limiting resistors). The PWM signal has a duty cycle which increases over the ramp period (settable with the pot) to fade-in the LEDs.
When the switch is opened the ramp voltage falls and hence the PWM duty cycle decreases over the same set period to fade-out the LEDs.
N.b C5 should be 220μF in practice, but to make the simulation run faster it is 22nF.