It's highly technical and I, as a layman, do not feel qualified to critique it. There's simply too much I do not understand - about the reliability of data collection, about modeling techniques, about what is acceptable theoretically and what is not. This is the first such technical paper I've read and I'll have to read it several more times simply to be able to talk about it comfortably.
But, you've asked for a layman's opinion and I'll give you mine. Lockwood begins by talking about the proposed mechanisms by which solar variations supposedly influence climate on earth. He discounts the 11 year solar cycle because it is modulated by the oceans and looks at longer trends in the relevant parameters. He finds that these are all in decline while global temperatures are rising and therefore they can not be use to explain what has happened in the last 25 to 40 years (or perhaps it would be better to say that they've moved in directions opposite to what one would expect if they were responsible for climate change during this period). He is at pains to point out that there's much we do not understand about extraterrestrial forcings and - in particular - about variations in solar activity so that no conclusions can be drawn about future correlations...or lack of. The heart of his argument - for me - lies in the last paragraph of section 4 and in section 5, conclusions.
I await the comments of the well-known climate skeptics with international reputations. Will they agree with him, or not? With what caveats? It is interesting that the first such person - the Israeli scientist mentioned in the Guardian - has had to propose a totally new mechanism (if the newspaper is to be believed). Not a very good start for the skeptics.
For the amateurs who think they've caught Lockwood in simple graphical or mathematical errors, in obvious omissions of well-known facts, or in believing results posted from ground-stations located next to large incinerators...I say seek professional help. The sooner the better.
What I hear a lot in this debate is that people may not understand the evidence, and the lack of understanding is not about to stop them from believing that manmade CO2 is warming the globe. If that's your position then you're in really good company.
This topic is just not nearly as mysterious as the grant-beggars like to get everyone to think, and I invite you to consider that the real reason that you don't follow what they're saying is because they actually aren't saying anything.
Feel free to ping me if there's any particular technical point you want me to go over with you. In the mean time please don't vote to raise my taxes before getting a better handle on the tech side of the debate.