Confusion with rate of fatigue

There's not a lot here to go on - i.e. your training volume, etc.  That said, you made a couple of comments that may be instructive.

Both of the comments I put in bold above imply to me you may be "going to hard" in training.  That leads to a question - how are you setting your training paces?  More specifically, have you determined your training zones for both running and cycling?  Ideally you'll be using Heart Rate (HR) for the run and power for the bike, although you can use HR on the bike also if you don't have a power-meter.

Here's a great article to help you determine your training zones - https://beginnertriathlete.com/cms/article-detail.asp?articleid=633

Once you've determined your training zones, as a "newbie" you'll want to be spending the bulk of your training time in zone 2.  That will likely feel slow if you've been running at race pace.  However, triathlon is an aerobic sport.  To get faster you need to develop your aerobic energy pathway and your bodies ability to utilize fat for fuel.  You do that with zone 2 training.

Hope that helps.

Your legs are getting wrecked on the bike because you're pushing more resistance than you have trained up to.  That's not necessarily a bad thing.  In general, you can get away with biking and swimming pretty hard since they don't punish the body like running does.  Running hard all the time will lead to excessive fatigue and higher injury risk.  Running after lifting weights probably makes the effort tougher too.

In general, I would:

Swim & bike moderate to hard most of the time and easy some of the time.  I would do 30-90 minutes of interval type work on the bike a couple times a week and get some moderately paced miles in on the weekend...anywhere from 20-60 depending on your appetite.  The longer ride on the weekend will build endurance while the interval work during the week will build power.

Run easy most of the time (80% or more until you're over 20-25 miles/week).  Running easy means conversational pace.  You need the easy miles to build endurance before you add in any speed work.  Btw, you will get faster if you do nothing more than a) run often...5-6 times a week and b) only run easy.  As a bonus, running easy keeps the fatigue level relatively low so you can execute your other workouts.

You didn't say anything about your weight.  If you're a bit bigger from the weight lifting it's going to negatively affect your climbing (bike) and running speed.