OP,
Your kids know something is wrong and are actively asking for an explanation. By lying you are gaslighting them, teaching them not to trust you, and not to trust their own instincts.
You should tell them soon. A lot of the research shows much of the damage to kids in divorce is actually before they are told, when there is tension in the house that kids don't understand.
On how to tell them, you should go for age-appropriate truth, along with lots of reassurances that you both love them, they will be able to spend lots of time with both of you, and none of it is their fault. (This last msg seem obvious to you, but kids tend to always even subconsciously, think it's their fault. And by the way, They are much more likely to guess that it is their fault, if you don't tell them the truth, because they will know it doesn't add up,
Explain that the romantic love is gone between you - certainly at least on your side. That you are sure it is not going to come back. That it is very hard for a couple to be happy in this situation. That it tends to cause fights/ unhappiness etc. That you have both been trying for a long time to make it better, but you know at this point that it won't get better. That there is nothing they can do about this and it is in no way their fault. That it's natural for them to feel sad or angry about any big change like this. That they may notice (as they already have) that you guys are also finding it hard. But that both their dad and you are going to be ok, and you will both be working really hard to make everything work ok for them.
Reassure them that lots will stay the same (list some stuff, if you know it - eg staying at the same school, having the same friends, still going to band practice on Mondays, still having movie night on Fridays...) including that you both love them and you are both still their parents and will both still spend lots of time with them. Invite their questions.