Property Transfer - Is it possible to use test case custom property in jsonpath expression textbox?

I am not sure how to do it in property transfer using condition.

However, you can use groovy step[property tranfer becomes obselete if you use groovy step] to do the same (if you are ok?):

/* this script reads a json and gets the lastUpdateDate where label is
* matching with test suite property called 'Property_Name'
*/
import net.sf.json.groovy.JsonSlurper
//Using static json, you can use dynamic response as well
def jsonText = '''{
    "response" : {
        "endRow" : 300,
        "totalRows" : 21938,
        "status" : 0,
        "startRow" : 0,
        "data" : [
        	  {
                "label" : "Property_Value",
                "lastUpdateDate" : "2014-08-13T15:48:56"
            }, 
            {
                "label" : "Property_Value2",
                "lastUpdateDate" : "2014-08-13T15:48:58"
            }, 
            {
                "label" : "Property_Value3",
                "lastUpdateDate" : "2014-08-13T15:49:01"
            }
        ]
    }
}'''
def response = new JsonSlurper().parseText(jsonText).response
def dateNeeded = response.data.find{it.label==context.testCase.testSuite.properties['Property_Name'].value}.lastUpdateDate
//setting the required date in 'DATE_FROM_PREVIOUS_RESPONSE' test case property and use it later steps like ${#TestCase#DATE_FROM_PREVIOUS_RESPONSE}
context.testCase.setPropertyValue('DATE_FROM_PREVIOUS_RESPONSE', dateNeeded)

If you want to use dynamic response from previous request step, replace following in the above snippet

from:

def jsonText = '''{
    "response" : {
        "endRow" : 300,
        "totalRows" : 21938,
        "status" : 0,
        "startRow" : 0,
        "data" : [
        	  {
                "label" : "Property_Value",
                "lastUpdateDate" : "2014-08-13T15:48:56"
            }, 
            {
                "label" : "Property_Value2",
                "lastUpdateDate" : "2014-08-13T15:48:58"
            }, 
            {
                "label" : "Property_Value3",
                "lastUpdateDate" : "2014-08-13T15:49:01"
            }
        ]
    }
}'''

to

//Replace the step name below.
def jsonText = context.testCase.testSteps['step1'].testRequest.response.responseContent

Hope this helps.