I think it was just as simple as we've been led to believe.
Here's the JMO scenario from Tilly's point of view:
Tilly and Lyle are known to themselves and to S&M to drive to and from work together. Tilly knows she will be with Lyle at the time she's supposed to be driving the getaway car. So do S&M. This is why they were originally going to go back to Tilly's house (this is JMO remember) and kill Lyle there, then leave with Tilly and ride off into the sunset (it was night, whatever.
)
Then Tilly got to feeling bad about this "kill Lyle" stuff she got all caught up, before it seemed so real. So she expressed this to S&M (JMO) and they said "don't worry Tilly, we have these pills we'll bring along with us. We can give them to him and he'll just fall asleep really soundly and sleep for hours and we can head out to begin our new lives together".
JMO she thought about her future life with her two male paramours who would be forever in her debt for their very freedom, and thought about her raging libido, and decided this was fair enough.
JMO Tilly was all set to carry through with this plan when she mistook her nervous excitement for a heart attack which caused a full-fledged panic attack which caused her to REALLY think it was a heart attack, and scared the bejezus out of Lyle and sent them to the hospital, where she turned off her cellphone intentionally and didn't touch it all night because every time she began to feel a little bit less like she was having a heart attack, she would think about them escaping without her being there and she'd panic again, so spent all night freaking out in the hospital (maybe even seeing or hearing about news of the escape on the hospital tv or from people talking in the halls, etc), only to have Lyle come check on her in the morning and hand her her phone upon discharge.
With him sitting there by her, she had to turn it on like she "normally" surely would, and that's when all the texts and things came flooding in saying that everyone wanted to get ahold of her because the men had escaped.
So she came up with the best lie for Lyle that she had - I didn't sleep with them - what's the most extreme way to swear to it so he'll definitely believe her in this all-important time in her life? swear on her son's life. Next important lie - I did whatever I did because I love you and didn't want to hurt you.
I really think this is that simple. JMO
All JMO.