Regarding your W's request to work things out at the kitchen table with her L friend, I would take her up on that offer. If you can work things out amicably it will pay huge dividends for you.
Just my opinion...
I originally thought I'd forgo having a lawyer because everything seemed so cut-and-dry and it didn't seem like it would be worth the cost of getting my own lawyer. I eventually decided to get a lawyer, largely because I felt like it would it would be a show of strength to have my own lawyer. By the time I was divorced, I was very thankful that I had my own lawyer.
Retaining a lawyer boosted my confidence and the lawyer explained the entire process so I was more relaxed while awaiting the actual divorce. In addition, my lawyer handled all the divorce communications between my wife's lawyer and the court system. I didn't have to worry about checking the mail and making sure the appropriate forms were filled-out. I was never served divorce papers because my lawyer handled everything. When mediation day came, everything went very smoothly, there was no stress, and I had a very good resolution.
I highly recommend retaining a lawyer unless you absolutely can't afford one. It's one more signal to your wife that you're ready to move on and that you'll be fine without her.