As you know, when you specify "output" of an operation as "new tab" you can set properties of the tab you open. One of the properties is "process name", where you can specify the process that will automatically run when the user selects a tab. Moreover, the context of the process will be automatically set to match the context that existed when the tab was initially opened.
So if the user initially clicked on a "customer", which resulted in a new tab running the DISPLAY LAYOUT operation, that customer will be remembered as context of the tab. So all you have to do is create a process that takes customer as input and sets this customer into LIRU:
LoggedInRegularUser.SelectedCustomer = Customer
Then you specify this process into the settings of the new tab. When the user switches between tabs this process will run and your existing LIRU-based solution should work
(this process is a replacement to the "script" John was talking about)