Generally, if you both hold by hands, try to extend pecs, raise shoulders, contract wrists and sometimes contract elbows too. This combination is usually very useful against a basic lift or shovel.
When it comes to advanced lifts, there is no distinct counter. It is very situational and highly depends on grab situation and momentum.
You can practice counters to these moves by opening aikido in singleplayer and lifting yourself with uke, then trying to make a counter move with tori and so on.