It's trickier doing this with code instead of lookups, but it should still be doable.

Here's a start...

This Javascript code is for the Layout Designer (not Classic Designer) and was tested on version 11.0.2311.50556.

Add 9 date fields to your form and 1 dropdown field to your form (you can leave the values on the dropdown blank, they'll be populated via the Javascript).
These fields can't be read-only or the Javascript won't be able to populate them (but you should still be able to disable them via Field Rules if you don't want the user to be able to edit them).
The date format of the date fields should be YYYY-MM-DD so that is matches what the script will be populating.
Mine looks like this:

You'll need the ID numbers for these 10 fields as those will be populated in lines 2-11 of the Javascript below.

The only other part of the Javascript you should need to edit is lines 14-18 - these five fields configure the pay period values for the year - in theory, this is the only part you will need to edit each year.

When the form is loaded, the Javascript creates an array of the dates automatically, and populates the fields with them.  The first 6 fields on the form are jsut informational fields that display the dates for the first and last pay period.  The dropdown field populates the selectors for the pay periods that were generated by the script.  And the last 3 date fields will populate based on what was selected from the drop-down.

//Variables for Fields
var firstBegin = 2;
var lastBegin = 5;
var firstEnd = 3;
var lastEnd = 6;
var firstPay = 1;
var lastPay = 4;
var periodDropDown = 7;
var selectedBegin = 10;
var selectedEnd = 11;
var selectedPay = 9;

//Variables for Pay Periods
var firstBeginDate = '2024-12-22T00:00:00';
var firstEndDate = '2025-01-04T00:00:00';
var firstPayDate = '2025-01-10T00:00:00';
var periodInDays = 14;
var periodCount = 26;

//Simple function to add n days to a date.
function addDays(date, days) {
  const newDate = new Date(date); // Create a new Date object to avoid mutating the original
  newDate.setDate(newDate.getDate() + days);
  return newDate;
}

//Create arrays for Dates
var beginDateArray = [];
var endDateArray = [];
var payDateArray = [];
for (let i = 0; i < periodCount; i++) {
  beginDateArray.push(addDays(Date.parse(firstBeginDate), (i * periodInDays)));
  endDateArray.push(addDays(Date.parse(firstEndDate), (i * periodInDays)));
  payDateArray.push(addDays(Date.parse(firstPayDate), (i * periodInDays)));
}

//Populate the First and Last Begin Date Fields
var dateString = {dateStr: beginDateArray[0].toISOString().slice(0, 10)};
LFForm.setFieldValues({fieldId: firstBegin}, dateString);
dateString = {dateStr: beginDateArray[(periodCount - 1)].toISOString().slice(0, 10)};
LFForm.setFieldValues({fieldId: lastBegin}, dateString);

//Populate the First and Last End Date Fields
dateString = {dateStr: endDateArray[0].toISOString().slice(0, 10)};
LFForm.setFieldValues({fieldId: firstEnd}, dateString);
dateString = {dateStr: endDateArray[(periodCount - 1)].toISOString().slice(0, 10)};
LFForm.setFieldValues({fieldId: lastEnd}, dateString);

//Populate the First and Last Pay Date Fields
dateString = {dateStr: payDateArray[0].toISOString().slice(0, 10)};
LFForm.setFieldValues({fieldId: firstPay}, dateString);
dateString = {dateStr: payDateArray[(periodCount - 1)].toISOString().slice(0, 10)};
LFForm.setFieldValues({fieldId: lastPay}, dateString);

//Populate the Options in the Select Pay Period Dropdown Field
var arrayForSelect = [];
for (let i = 0; i < periodCount; i++) {
  var element = {label: "P" + (i + 1), value: (i + 1)};
  arrayForSelect.push(element);
}
LFForm.changeFieldOptions( { fieldId: periodDropDown }, arrayForSelect, "replace" );

//When the selected pay period changes,
//update the three selected date fields.
LFForm.onFieldChange(function() {
  var selectedPeriod = LFForm.getFieldValues({fieldId: periodDropDown});
  var selectedBeginDate = {dateStr: beginDateArray[(selectedPeriod - 1)].toISOString().slice(0, 10)};
  LFForm.setFieldValues({fieldId: selectedBegin}, selectedBeginDate);
  var selectedEndDate = {dateStr: endDateArray[(selectedPeriod - 1)].toISOString().slice(0, 10)};
  LFForm.setFieldValues({fieldId: selectedEnd}, selectedEndDate);
  var selectedPayDate = {dateStr: payDateArray[(selectedPeriod - 1)].toISOString().slice(0, 10)};
  LFForm.setFieldValues({fieldId: selectedPay}, selectedPayDate);
}, {fieldId: periodDropDown});