Parsing inflected forms may not always work as expected. If the following does not give the correct word, try Latin Words or Perseus.
lūdĭa, ae, f. [1. ludius]. 
- I.  An actress, a female stage-dancer, Mart. 5, 25, 10.
 
- II.  A female gladiator, a gladiator’s wife or mistress: quid vidit, propter quod ludia dici Sustinuit, Juv. 6, 103: quae ludia sumpserit umquam hos habitus? id. 6, 266.