Your two moon signs are close together in Semi-sextile relation (30deg ).
There is some chance that you may get along. Usually the Leo Moon in this relationship is tolerant than the other. The Leo moon is generally very emotional compared to the mentally driven Virgo Moon. Be aware that the Leo Moon will tend to feel things from an emotional aspect, while the Virgo Moon will feel them mentally.
There is some chance that you will get along, to create a strong relation. One thing to watch out for with this type of relationship is that you may notice that your negative feelings are twice as strong when you are in a relationship with this person. Since both of you feel nearly the same in many situations you may both feel negatively at the same time and cause even more bad feelings to flow between you.