Does it make sense to attribute a percentage of organic installs to paid for LAT users?

It absolutely makes sense! If you think about how Direct Response advertising works in more traditional channels like TV or Out-Of-Home it is actually the only way to measure results: you measure the revenue uplift that was generated for your "organic" visitors in the targeted market (usually time-boxed). I can recommend reading up on "Incrementality" as well, e.g. here: https://www.nanigans.com/2018/04/18/from-attribution-to-incrementality-5-steps-to-start-growing-revenue/