Hi and welcome to LOC.
First thing to do is get the fault code that the eml is producing an post it on here. Ask the garage for the exact code the fault reader is giving or even better have a look yourself when it's plugged into a diagnostic machine/code reader. Without the fault code it's total guesswork. My experience is faulty plugs won't give an engine warning light but a faulty coil pack certainly will.
The exhaust ticking like mad after turning the engine off is normal, it's the CAT's cooling down.
£200 to change spark plugs is crazy money mate. Set of 6 is £50-£60 and a mechanic can change them in about 15-20 mins. Even I can change them in half an hour and have a cup of tea lol
With no history of the timing belt then it's up to you if you risk it or change it. If it was done by Lexus there will be a date stamp in the engine cover somewhere with the date, dealership and mechanics initials and mileage at the change. The fact it's moved suggests if the belt was replaced the tensioner and idler wasn't changed. Personally I'd change it along with the tensioner and idler. Also maybe the timing is out, that's what's causing all the grief?
I really wouldn't be thinking about engine swaps right now. Get the fault codes and get to the bottom of this. At 88,000 miles there's no way that engine should be in need of a rebuild. Valve stem seals isn't that bad a job, cost you in labour not parts.
My advice would be to get it diagnosed either buy someone you trust or Lexus. Lexus will charge you about £45 for a full diagnostic and then at least you know the exact problem and what exactly needs replacing. You don't have to get Lexus to do it, say no thanks, pay for the diagnostic and go off and get the job done cheaper.
Anyway hope this helps a little. These really are cracking cars when driving right. I've had more than my fair share of probs with mine but what can I say, I blooming love this car!! :)