The software does handle double sided boards. The component coordinates given by most (all?) CAD systems are as seen from top. When the board is placed on the table the origin, normally on bottom left, goes to bottom right. Also, the X coordinates used by a pick and place machine will be negative. The board size is not included in the pick and place file. Therefore:
When placing bottom side on double sided boards, you need to put board X size to Job Offset X field as a negative value. This will keep the origin in the same place that it is on the CAD system, but since you are looking the board from the other side than the CAD program, the nominal X coordinates will be negative.
The recommended method to build double sided boards with LitePlacer is to design the board so, that bottom side has only passives and other small components. Populate and solder the bottom side first. Then support the board on a jig or pegs and populate the top side. The software does measure placement height automatically. The surface tension of molten solder is high and will keep the bottom side components from falling off during top side reflow. All “normal” passive components will tolerate two reflow cycles.
When building double sided boards, factories use glue to keep bigger components attached to the board bottom side during reflow. The LitePlacer does not do glue dispensing, so this is not very practical. Therefore, relays, connectors or ICs (due to the relatively small surface area of legs) are not recommended on bottom side.