lightning:layout horizontalAlign left and right

horizontalAlign is used to position the grid elements within the grid, not for aligning content, which I suspect is your intent.

If you want to align the individual child elements, use normal CSS for that:

<aura:component>
    <lightning:layout>
        <lightning:layoutItem size="8" class="left-align">
            ... Left Content ...
        </lightning:layoutItem>
        <lightning:layoutItem size="4" class="right-align">
            ... Right Content ...
        </lightning:layoutItem>
    </lightning:layout> 
</aura:component>

---

.THIS .left-align {
    text-align: left;
}
.THIS .right-align {
    text-align: right;
}