Do haploid organisms have meiosis in their lifecycle? If yes, state when does it

occur?

Yes , haploid organisms also have a meiosis in their life cycles. Normally diploid organisms only undergo meiosis. But in some haploid organisms undergoing sexual reproduction, to haploid gametes fuse to give rise to diploid zygote. The zygote then undergoes meiosis to produce haploid organism. 

That is, the haploid plant produces gametes by mitosis. This plant body represents a gametophyte. Following fertilisation, the zygote also divides by mitosis to produce a diploid sporophytic plant body.  Haploid spores are produced by this plant body by meiosis. These in turn, divide by mitosis to form a haploid plant body once again.