I have a SharePoint list [Project List] with few columns like Title,Project Start Date and Project end date.In another SharePoint list [Project Task list] and I have to format the list view to a Gantt chart view with JSON code.But Here, my problem is to include the Project Start Date and Project End Date columns from the Project list as look up columns.How to include them in Json code of mine?

{
  "$schema": ".schema.json",
  "hideSelection": true,
  "hideColumnHeader": true,
  "rowFormatter": {
    "elmType": "div",
    "style": {
      "height": "=if(@rowIndex == 0, '88px', '52px')",
      "display": "block",
      "width": "100%",
      "position": "sticky"
    },
    "attributes": {
      "class": "ms-bgColor-neutralLighter--hover"
    },
    "children": [
      {
        "elmType": "div",
        "attributes": {
          "class": "ms-bgColor-themePrimary"
        },
        "style": {
          "width": "100%",
          "display": "=if(@rowIndex == 0, 'flex', 'none')",
          "height": "36px",
          "padding": "0",
          "font-weight": "bold",
          "border-radius": "6px 6px 0 0"
        },
        "children": [
          {
            "elmType": "div",
            "txtContent": "Milestone Chart",
            "style": {
              "width": "220px",
              "text-align": "left",
              "padding-left": "0.4em",
              "box-sizing": "border-box"
            },
            "attributes": {
              "class": "ms-fontSize-16 ms-fontColor-white"
            }
          },
          {
            "elmType": "div",
            "style": {
              "flex-grow": "1",
              "height": "100%",
              "position": "relative"
            },
            "children": [
              {
                "elmType": "div",
                "txtContent": "=**toLocaleDateString([$ProjectStart])"**,
                "style": {
                  "position": "absolute",
                  "padding": "14px 4px 0 4px",
                  "height": "22px",
                  "border-radius": "6px 6px 0 0"
                },
                "attributes": {
                  "title": "='Project Start: ' + **toLocaleDateString([$ProjectStart])**",
                  "class": "ms-bgColor-themeDarker ms-fontSize-14 ms-fontColor-white"
                }
              },
              {
                "elmType": "div",
                "txtContent": "=toLocaleDateString([$ProjectDue])",
                "style": {
                  "position": "absolute",
                  "right": "0",
                  "padding": "14px 4px 0 4px",
                  "height": "22px",
                  "border-radius": "6px 6px 0 0"
                },
                "attributes": {
                  "title": "='Project Finish: ' + toLocaleDateString([$ProjectDue])",
                  "class": "ms-bgColor-themeDarker ms-fontSize-14 ms-fontColor-white"
                }
              },
              {
                "elmType": "span",
                "txtContent": "=toLocaleDateString( @now)",
                "style": {
                  "position": "relative",
                  "width": "90px",
                  "z-index": "100",
                  "display": "=if([$ProjectDue] < @now , 'none', 'block')",
                  "left": "=floor( (Number(@now)-Number([$ProjectStart])) / (Number([$ProjectDue])-Number([$ProjectStart])) * 100 ) + '%'",
                  "background-color": "#e1dfdd",
                  "text-align": "center",
                  "padding": "0 3px",
                  "margin": "0 0 0 3px"
                }
              },
              {
                "elmType": "span",
                "attributes": {
                  "class": "ms-fontColor-gray40"
                },
                "style": {
                  "position": "relative",
                  "display": "=if( [$ProjectDue] < @now , 'none', 'block')",
                  "top": "-1.3em",
                  "z-index": "1",
                  "border-left": "5px solid",
                  "height": "800px",
                  "width": "0.1em",
                  "left": "=  (Number(@now)-Number([$ProjectStart])) /  (Number([$ProjectDue])-Number([$ProjectStart]))  * 100  + '%' "
                }
              }
            ]
          }
        ]
      }