I lactose intollerant, can i take probiotic lactobacilus ? or it will trigger my allergy ?

No problem: They are not related problem. In fact, probiotic and prebiotic supplements are being studied for their role in reducing allergic diseases. Thus far, eczema (atopic dermatitis) appears to be the condition responding to these supplements, but researches are still underway.

Lactose intolerance: I see your confusion but lactobacillus is a probiotic bacteria, not a sugar. Lactose intolerance (difficulty digesting milk sugar) can be secondary to lactase enzyme deficiency, or due to a bigger problem of small bowel inflammation, infection, infiltrative disease, and/or maldigestion. Don't assume its lactose intolerance unless tested, or at least assessed response to lactase enzyme replacement.