Can you trigger an AWS Lambda on a dynamic timer?

This can be accomplished by setting a CloudWatch event rule to trigger your Lambda function. On each invocation of your Lambda function, the function will need to determine its next run time and modify the event rule appropriately.

var AWS = require("aws-sdk");

exports.handler = function(event, context) {
    var cloudwatchevents = new AWS.CloudWatchEvents();
    var intervals = Array(3, 5, 7);
    var nextInterval = intervals[Math.floor(Math.random()*intervals.length)];
    var currentTime = new Date().getTime(); // UTC Time
    var nextTime = dateAdd(currentTime, "minute", nextInterval);
    var nextMinutes = nextTime.getMinutes();
    var nextHours = nextTime.getHours();

    //  =================================
    //  DO YOUR WORK HERE
    //  =================================

    var scheduleExpression = "cron(" + nextMinutes + " " + nextHours + " * * ? *)";
    var params = {
        Name: "YOUR CLOUDWATCH EVENT RULE NAME",
        ScheduleExpression: scheduleExpression
    };
    cloudwatchevents.putRule(params, function(err, data) {
        if (err) {
            console.log(err, err.stack);  
        }
        else {
            console.log(data);
        }
    })
};

var dateAdd = function(date, interval, units) {
    var ret = new Date(date); // don't change original date
    switch(interval.toLowerCase()) {
        case 'year'   :  ret.setFullYear(ret.getFullYear() + units);  break;
        case 'quarter':  ret.setMonth(ret.getMonth() + 3*units);  break;
        case 'month'  :  ret.setMonth(ret.getMonth() + units);  break;
        case 'week'   :  ret.setDate(ret.getDate() + 7*units);  break;
        case 'day'    :  ret.setDate(ret.getDate() + units);  break;
        case 'hour'   :  ret.setTime(ret.getTime() + units*3600000);  break;
        case 'minute' :  ret.setTime(ret.getTime() + units*60000);  break;
        case 'second' :  ret.setTime(ret.getTime() + units*1000);  break;
        default       :  ret = undefined;  break;
    }
    return ret;
}

You should be able to swap my random determination with your own scheduling logic and insert whatever work you need in place of my comment.

You will need to substitute your event rule's name for "YOUR CLOUDWATCH EVENT RULE NAME" in my snippet.

Great question for a blog: AWS Lambda Functions That Dynamically Schedule Their Next Runtime

This can now be accomplished without polling using a step function. You can find more information on AWS, but basically you would define a state machine for your step function that uses the Wait state and the TimestampPath field. Your state machine might end up looking something like

{
  "SartAt": "WaitState",
  "States": {
    "WaitState":     {
      "Type":          "Wait",
      "TimestampPath": "$.timestamp",
      "Next":          "ExecuteLambda"
    },
    "ExecuteLambda": {
      "Type":          "Task",
      "Resource":      "lambda-arn",
      "End":           true,
      "Retry":         [
        { ... },
        ...
      ]
  }
}

Assuming you're using Node, you could then invoke the step function with the following code:

const AWS = require('aws-sdk');

const stepFunctions = new AWS.StepFunctions();

await stepFunctions.startExecution({
  stateMachineArn: process.env.STATE_MACHINE_ARN,
  name:            "unique-name",
  input:           JSON.stringify({
    timestamp: (new Date(/*Date you want to start execution*/)).toISOString(),
    // Any extra context you want to pass to the step function.
  }),
}).promise();