If the base line of the rows in the second column never match the ones in the first column then you will need two tables side-by-side. As you are going to pretend they are the same table you want them grouped in a frame.
Click Insert > Frame > Frame Interactively and draw a frame big enough to take both tables.
Select the frame by the edge, right-click and select Properties, select the tab labelled Columns and choose 2 columns, OK.
Click elsewhere to deselect the frame. Click inside the frame and create your first table with row heights as you want.
Click below the first table (within the frame) the in the main menu, click Insert > More Breaks > Insert Column Break (or Ctrl+Shift+Enter). Create your second table in the second column with row heights as you want.
Adjust borders as required.
TwoTablesInFrame.odt