Hi @Gines,
First of all, you need to notice that the Title field in List1 need to have enforced unique value. Otherwise, when you have one value from Lookup column in List 2, it could point to multiple items corresponding in List 1.
If your Title field in List1 has unique values, then this could be achieved by following below steps:
1. Create the auto-generated app using List 2 as the connection.
2. Insert a new screen, name it "DetailScreen2". In this screen, insert a display form, and set its DataSource property to:
'List 1'
Set its Items property to:
First(Filter('List 1',Title=DataCardValue30.Selected.Value))
Notice that DataCardValue30 is the control name of the Lookup column data card on DetailScreen1.

3. On DetailScreen1, insert a button and set its OnSelect property to:
Navigate(DetailScreen2,None)
I just tested and this works.

About the search box, did you mean search for Gallery control? If so, then notice that Search Function supports only string searches. That means that you can use it with text column, but not with Person and Group column. But you can use Filter / Lookup functions which could work with Person and Group fields. The formula could be something like:
Filter('List 2', StartsWith( Title,TextSearchBox1.Text ) || StartsWith( Person.DisplayName, TextSearchBox1.Text ) )
This filters the 'List 2' data source for records in which either the Title column or the Person column starts with the search string in TextSearchBox1 textinput control. The || operator is true if either StartsWith function is true.
Regards,
Mona