Salvete
I’m working my way through this chapter and have come across this. My understanding based on the context is that it means ‘Medus embraces her’. My question is, how is this a passive act. Why is it not, ‘Medus eam complectit’?
I hope my question is not inane. All help is appreciated and thanks for your patience.
According to the dictionary, complector is a deponent verb:
And if you continue reading the chapter, and go to the end, you will see that in the GRAMMATICA LATINA section, this new form of verbs is explained… 
These verbs look weird, but if it may make sense if you consider them as bearing some reflexive meaning (it works for most of them). For example, complectitur is basically from com + the verb plectere, which means something like « to bend ». With the deponent form, it becomes obvious that « Mēdus bends himself around Lȳdia ».
I just realised that I’d never said thank you for the informative replies.
Sorry about that.
I’m ever so grateful for the help received. All such pointers help feed my enthusiasm and augment my pleasure. Thank you.
Valete