"It's been too long"
There's a point in every lapsed friendship where the gap itself becomes the obstacle. At two months you could have sent "lunch next week?" and it would have been nothing. At fourteen months it seems to need a preamble. You'd have to acknowledge the silence, explain it and apologise for it. You start drafting in your head. "I'm so sorry I've been useless at keeping in touch, things have been mad, I kept meaning to message and then so much time had gone by that..." It's exhausting before you've typed a word, so you don't.
The gap produces embarrassment, and the embarrassment makes the gap longer. Next month it'll be fifteen months, and the imagined preamble will be longer still.
Aknin and Sandstrom's studies offer a clue to what's happening. They found that people were less willing to contact old friends who felt more like strangers to them. Time does that. A friend you haven't spoken to for a year has drifted, in your mind, some way towards the category of people you don't know. You don't know what their days are like any more, or whether the job turned out well, or what's happened with their father's health. Approaching them starts to feel like approaching a stranger, and chapter 4 described how reluctant people are to do that.
But your friend isn't a stranger. Two minutes into a conversation you'd find that the old ease was intact, as it is when you run into someone in the street. The sense of strangeness comes from the silence, and the person hasn't changed. Most people have had the experience of meeting an old friend after years and finding it was as if no time had passed. People say it with surprise every time, which suggests that the expectation of awkwardness is reliably wrong.
Here are three things about the gap that I think are true and that the embarrassment hides. These are my own reasoning.
The first is that the gap belongs to both of you. You're mortified about your fourteen months of silence. Your friend has been silent for the same fourteen months. If anyone is owed an apology, each of you owes the other the same one, and they cancel out. Your friend knows this perfectly well. If you open with a long apology, the most likely reply is "don't be daft, I've been just as bad".
The second is that long gaps are normal and everyone knows it. Adult friendships run like this. People change jobs, have children, move and go through bad patches, and contact lapses for a year or three. Hardly anyone past thirty has a record of unbroken contact with anybody outside their household. Your friend won't read a fourteen-month gap as an insult. They'll read it as life, because that's what their own gaps with other people have been.
The third is that the explanation you think you owe isn't wanted. Imagine receiving two messages from an old friend. One says, "I'm so sorry for being rubbish, I've been meaning to get in touch for ages, things have been really hectic and I feel terrible about it." The other says, "I walked past that sandwich place today and thought of you. How are you?" The first makes you do work. You have to reassure them. The second is a pleasure to get. It carries all the information that matters, which is that they thought of you warmly.
So what I'd suggest is that you don't mention the gap, or that you give it one light clause at most. "It's been far too long" is plenty. Then go straight to the present, with what made you think of them and how they are. Chapter 12 has examples.
One objection is that it's been much longer than fourteen months. "It's been eleven years. We were close at university and I haven't spoken to her since her wedding." The same reasoning holds, and chapter 4 suggests the pleasure on the other end may be greater, because the surprise is greater. An old friend from eleven years ago who writes two warm lines has done something lovely. You might not pick the friendship back up. Lives diverge. But the message itself will almost certainly be welcome, and you'll have found out.
There's a last thing to weigh, and I say it without wishing to alarm you. The gap only ever goes in one direction. There won't be a future date when fourteen months has become a more comfortable number. If it feels too long now, the message will never be easier to send than it is today.