Sadly there is no way of doing a relationships in PowerApps like you would in SQL. You have to use a couple of different methods to manipulate the data.
I am guessing / assuming you are placing your drop down on an edit form which has its "DataSource" set to your "custtable", your are using "Item" to select a row from that table and your drop down has been placed on a card which is has it "field" set as "party".
On your drop down you need to set three properties items, update, default.
Items needs to be populated from "direpartytable" using ShowColumns. Something like..
ShowColumns('direpartytable', "DisplayName" , "recid")
The the "Update" needs setting to save the recid and not the DisplayName. Something like..
Dropdown.Selected.recid
The "Default" needs changing so the current field value of party in the custtable is displayed. Otherwise its is set to '1' which just displays the first time in the list. Something like this...
LookUp('direpartytable', recid=ThisItem.party, DisplayName)
LookUp
ShowColumns
I have found lookups quite slow so, I only use them where I really need need to and creating sql views on the server for any relational data coming from multiple table.
Shane Young has done some really helpful videos on PowerApps you should take a look this.
youTube - PowerApps SQL LookUps and Relationships