The size attribute on the Lightning:layoutItem allows you to control the size of the item and, with multiple rows, the cards can span across various rows.
Let's use the following code in a Lightning Application created via the Developer Console:
<aura:application extends="force:slds"> <Lightning:layout verticalAlign="start" multipleRows="true"> <Lightning:layoutItem flexibility="auto" padding="around-small" size="6"> <Lightning:card title="1"> <p class="slds-p-horizontal_small"> Card 1 </p> </Lightning:card> </Lightning:layoutItem> <Lightning:layoutItem flexibility="auto" size="6" padding="around-small"> <Lightning:card title="2"> <p class="slds-p-horizontal_small"> ...