Hi Not necessarily to be honest. SharePoint has certain delegable types. "=" Is the best in my opinion, but since the lookup field is a complex field that consists of an ID and a VALUE it requires extra attributes.
However if you would like to filter a lookup field it would most likely be something like Filter(SharePointList, SharePointLookupField.Value = SearchTextBlx1.Text)...Something to that extent.
Once again you put the formula into the textInput Default property, this can't work. The TextInput default property expects a string because it is the default text inside the TextInput, you can't use a filter function here.
You have to select your gallery, and set the Items property to set the filter. Gallery.Items : Filter(...) Your filter seems correct now, you just have to put the formula in the right place.
Filtering a LookUp works fine only if you have less than 500 (up to 2000) items in your list because of the delegation. Otherwise you'll have to find a workaround.