The design is the visual features of the ILLUMINATED LIGHTING CONTROL DEVICE shown in solid lines in the drawings, whether those features are of shape, configuration, ornament, or pattern, or are a combination of any of these features. The portions of the article shown in stippled lines do not form part of the design. Gray shading is used in the drawings to represent illumination, wherein darker and lighter gray shading represent contrasting tones. The gray shading does not represent any particular color. In each of the design and the six variants, the design sequentially transitions from the first state to the last state in the sequence. The period with which one image transitions to another image forms no part of the design. The second, fourth and sixth variants are the reverse sequences of the first, third and fifth variants. Drawings of the design are included. FIG. 1 is a front perspective view of an illuminated lighting control device in a first state in a sequence; FIG. 2 is a front view thereof; FIG. 3 is a left side thereof; FIG. 4 is a right side thereof; FIG. 5 is a top view thereof; FIG. 6 is a bottom view thereof; FIG. 7 is a front view of the illuminated lighting control device of FIG. 1 in a second state in the sequence; FIG. 8 is a front view of the illuminated lighting control device of FIG. 1 in a third state in the sequence; FIG. 9 is a front view of the illuminated lighting control device of FIG. 1 in a fourth state in the sequence; FIG. 10 is a front view of the illuminated lighting control device of FIG. 1 in a fifth state in the sequence; FIG. 11 is a front perspective view of an illuminated lighting control device in a first state in a sequence, according to a first variant; FIG. 12 is a front view of the illuminated lighting control device of FIG. 11; FIG. 13 is a front view of the illuminated lighting control device of FIG. 11 in a second state in the sequence; FIG. 14 is a front view of the illuminated lighting control device of FIG. 11 in a third state in the sequence; FIG. 15 is a front view of an illuminated lighting control device in a first state in a sequence, according to a second variant; FIG. 16 is a front view of the illuminated lighting control device of FIG. 15 in a second state in the sequence; FIG. 17 is a front view of the illuminated lighting control device of FIG. 15 in a third state in the sequence; FIG. 18 is a front perspective view of an illuminated control device in a first state in a sequence, according to a third variant; FIG. 19 is a front view of the illuminated lighting control device of FIG. 18; FIG. 20 is a front view of the illuminated lighting control device of FIG. 18 in a second state in the sequence; FIG. 21 is a front view of the illuminated lighting control device of FIG. 18 in a third state in the sequence; FIG. 22 is a front view of the illuminated lighting control device of FIG. 18 in a fourth state in the sequence; FIG. 23 is a front view of the illuminated lighting control device of FIG. 18 in a fifth state in the sequence; FIG. 24 is a front view of the illuminated lighting control device of FIG. 18 in a sixth state in the sequence; FIG. 25 is a front view of an illuminated lighting control device in a first state in a sequence, according to a fourth variant; FIG. 26 is a front view of the illuminated lighting control device of FIG. 25 in a second state in the sequence; FIG. 27 is a front view of the illuminated lighting control device of FIG. 25 in a third state in the sequence; FIG. 28 is a front view of the illuminated lighting control device of FIG. 25 in a fourth state in the sequence; FIG. 29 is a front view of the illuminated lighting control device of FIG. 25 in a fifth state in the sequence; FIG. 30 is a front view of the illuminated lighting control device of FIG. 25 in a sixth state in the sequence; FIG. 31 is a front perspective view of an illuminated lighting control device in a first state in a sequence, according to a fifth variant; FIG. 32 is a front view of the illuminated lighting control device of FIG. 31; FIG. 33 is a front view of the illuminated lighting control device of FIG. 31 in a second state in the sequence; FIG. 34 is a front view of an illuminated lighting control device of FIG. 31 in a third state in the sequence; FIG. 35 is a front view of an illuminated lighting control device in a first state in a sequence, according to a sixth variant; FIG. 36 is a front view of the illuminated lighting control device of FIG. 35 in a second state in the sequence; and FIG. 37 is a front view of the illuminated lighting control device of FIG. 35 in a third state in the sequence.