Trough cross bedding isn't restricted to sandstones. This sedimentary structure forms through the migration of dunes in subareal or subaqueous environments. There are some spectacular trough cross beds in some of the Mississipian limestone units in southern Indiana (USA). There, oolites and skeletal grains were washed around as dunes in shallow marine environments and perhaps even eolian dunes behind beaches. I have attached a photograph from SEPM.ORG of the cross bedded Miami Oolite (Pleistocene) in Florida, USA.
Here is one example of trough cross bedding in terrigenous fluvial deposits with Miocene age from South-West Bulgaria, Blagoevgrad graben. The source of this sediments is slow moving river, with substential dimencions and meandering to straight canal, with often occurance of overflooding of the flood plain. Probably it were deposited in the lower part of the drainage basins. The iron oxides well presented in it, suggesting moderate warm and humid climate.
Cross bedding or any other bed form (or in general structure) in rock record should be studied in the context of hydrodynamic conditions of the encompassing sedimentary environment. Therefore, when we talk about cross bedding in carbonates we have to consider an environment where continuous movement of water body (if not wind-related) and traction can occur. This is needed to build migrating dune/ripples which give rise to formation of cross beds. Such conditions in generally calm environment of carbonate deposition can be found in shallow tidal channels and (oolite) shoals both of which generally interact and co-exist. In such environments identified cross beds predominantly depict bidirectional orientation of cross beds whose strike implies the direction of paleo-coasline. etc etc...
Excellent example of that can be found in present day oolitic shoals of Abu-Dhabi and Khuff reservoir as ancient analogue.