Is it easier for males or females to get into the top LACs? (Swarthmore, Williams, Amherst)
There’s really no difference, unless you’re talking about LACs like Vassar or Smith, where women definitely have the advantage.
Actually Smith is all women. Vassar was all women until fairly recently and men have an advantage applying there
There is little advantage in being a male or female. Race, however, might be a much bigger factor.
Look at section C1 of the Common Data Sets of the schools you are interested in. I looked at the 2014 CDS for each of the three mentioned and calculated the admit rates by sex:
Amherst: male 14.8%, female 13%
Swarthmore: male 19.6%, female 15.2%
Williams: male 20.9%, female 17.9%
Pomona: male 15.2%, female 10.2% My D is Pomona '19 so of course I think it’s the #1 LAC 
Typically LAC’s get more apps from women. Assuming they try to keep the enrolled class close to 50/50, that necessarily results in a lower admit rate for women. But it can certainly vary from school to school (at Harvey Mudd for example, the admit rate for women is higher) so look at the CDS for the school in question.
So males have an ever so slight advantage. Is the disadvantage for asians as big at the top LACs as it is at the top research universities (Duke, Harvard, Princeton)?
I would say the advantage to males is more than slight at many of these schools. Nationally females are attending college at a reasonably higher rate than men (something like 55:45) and graduating with an even higher skewing (getting close to 60:40). Many schools are typically seeing entering classes along these 55:45 lines or even more lopsided. My alma mater Tulane, for example, has been running 57:43 or higher for most of the last 5-7 years. Perhaps it is significant that Tulane is also considered to continue to emphasize the Liberal Arts a bit more than some research schools these days. In any case, they and all schools of course would prefer something closer to 50:50 if possible. So men do have some advantage. Now I am not saying it is a large advantage at any school, but I would go further at some of these LAC’s than “ever so slight”.
As far as the Asian issue, my impression is that this is not the same at LAC’s at all. It has been documented that the percentage of Asians that choose a STEM field for a major is quite high, and the tendency is to apply to research universities. So while I am mostly using deductive reasoning rather than basing this on any hard statistics or specific studies/articles addressing this issue exactly, it seems fairly certain that it just is not the same phenomenon at top LAC’s. Supporting that is one set of statistics, the fact that the percentage of declared Asians at the schools listed in post #4 is less than at the schools you mention, and I would say significantly. Amherst = 13%; Swarthmore = 16%; Williams = 10.9%; Pomona = 13%. As compared to Harvard = 18.8%; Princeton = 21%; Duke = 21.2% So it would appear that there is no reason to think Asian students are being “capped” at these LAC’s, although this does not constitute proof.
Best of luck!
Vassar became co-ed in 1969. Hardly “fairly recently”, unless you would say the same thing about Princeton!
@joesmith15 It depends on which school. Colgate & Colby for example it is harder for male applicants, while at Swarthmore, Middlebury, Bates and Bowdoin it is substantially harder for female applicants.
Asians have an advantage at all of them compared to many other schools, but at some they have a very big advantage because the population of Asian students is very low. I believe at Colgate that Asian students are just 3% of the student population. Many are substantially less than 10%. It seems to correlate to geography.
[The Washington Post](https://www.washingtonpost.com/posteverything/wp/2015/07/30/achieving-perfect-gender-balance-on-campus-isnt-that-important-ending-private-colleges-affirmative-action-for-men-is/) reckons that it twice as hard for a girl to get into Vassar as a boy. They are dismissive of the importance of gender balance, though, which I disagree with: they think that it is not a disadvantage to have a significant imbalance. That may be true for male dominant schools, but given how many times I have seen it mentioned here on CC I think it is real disadvantage to be perceived as female dominant (cf Vassar).
Vassar’s male/female ratio is similar to most LACs. In fact, there are several colleges with more skewed ratios (Macalester 39/61, for example). Gender imbalance isn’t limited to LACs either. Tulane’s ratio is 41% male…
@joesmith15, here’s a list (non-exhaustive) of schools where male applicants have an edge over females. Many LACs are on the list, but there are others that will surprise you too, including Brown, Tufts and Yale.
https://www.college-kickstart.com/blog/item/colleges-with-better-admission-odds-for-guys
On the flip side, the odds are often better for female applicants interested in the STEM fields.
https://www.college-kickstart.com/blog/item/colleges-where-female-applicants-have-an-edge