I have no experience with datalakes itself, but might work similar to AdvertisingAnalytics.
First, if you do not need it in a datalake by requirement, I would suggest you use Advertising Analytics. Basically you append a custom parameter at each Adwords Link which allows to connect backend data from AdWords.
See here: Advertising Analytics Overview
If you really want it in a data lake, either use above setup (and use the parameters as they are already available) or setup something yourself.
For a custom setup define a generic link parameter for each adwords campaign. you can use the generic parameters as described here: List of All ValueTrack Parameters in Google AdWords - Karooya basically you add the generic parameter in the top level of you accounts to append on any link.
next, track those URL parameters from the user in any analytics variable you want.
and finally, download both adobe analytics data as well as adwords data and match on the "parameter".