I had a brief look at the literature about a month ago and didn't find much. There is some evidence of performance enhancement from practicing motor tasks in lucid dreams (Erlacher, 2010), but the mechanism is unknown. Stumbrys et al. had two very speculative studies on asking dream characters within lucid dreams for help with problem solving (2010, 2011); they concluded that dream characters are terrible at arithmetic, but may be able to help with 'creative' tasks (I don't see good evidence for that from their data).

On lucid dream induction, Stumbrys et al. (2012) is a useful review.

Erlacher's abstract (emphasis mine):

Nocturnal dreams can be considered as a kind of simulation of the real world on a higher cognitive level. Within lucid dreams, the dreamer is able to control the ongoing dream content and is free to do what he or she wants. In this pilot study, the possibility of practicing a simple motor task in a lucid dream was studied. Forty participants were assigned to a lucid dream practice group, a physical practice group and a control group. The motor task was to toss 10-cent coins into a cup and hit as many as possible out of 20 tosses. Waking performance was measured in the evening and on the next morning by the participants at home. The 20 volunteers in the lucid dream practice group attempted to carry out the motor task in a lucid dream on a single night. Seven participants succeeded in having a lucid dream and practiced the experimental task. This group of seven showed a significant improvement in performance (from 3.7 to 5.3); the other 13 subjects showed no improvement (from 3.4 to 2.9). Comparing all four groups, the physical practice group demonstrated the highest enhancement in performance followed by the successful lucid dream practice group. Both groups had statistically significant higher improvements in contrast to the nondreaming group and the control group. Even though the experimental design is not able to explain if specific effects (motor learning) or unspecific effects (motivation) caused the improvement, the results of this study showed that rehearsing in a lucid dream enhances subsequent performance in wakefulness. To clarify the factors which increased performance after lucid dream practice and to control for confounding factors, it is suggested that sleep laboratory studies should be conducted in the future. The possibilities of lucid dream practice for professional sports will be discussed.