Contrary to popular belief, much of the gay intercourse in ancient Greece was not penetrative. That is to say, it wasn't anal sex. It was thigh sex. Hear me out.

To be penetrated was perceived to be a feminine act and therefore a male penetrating another male was often perceived to be an insult as this made one man out to be a woman.

Thigh sex on the other hand (the bottom holds his thighs together while the top pushes his penis between them, often with lubrication) was the more acceptable method of sexual intercourse between males. Theres even a word for it: intercrural sex. (Also: interfemoral intercourse)

The majority of pottery depicting homosexual relations shows intercrural sex but a small amount does show anal sex. However, if simply from the volume of sources, it is assumed that intercrural sex was the more popular method in both Greek and in Roman homosexual relationships. The word intercrural itself comes from the latin - crura meaning legs.

This also accounts for the number of literary sources for gay relationships where one speaks of his lover's thighs. Achillies mourns the loss of Patroclus and the "god fearing converse with your thighs". It was once assumed that this was a euphemism, but now we know it has the literal meaning of thigh sex.

For Ancient Egypt, information of this kind is too scarce to make any profound statement. There are a few paintings that could depict anal sex, but those are mostly small fragments or paintings that aren't really all that detailed, so one could never say for sure. BM EA 50714 is an example of this, where obviously two persons are having intercourse, possibly anal - but it's not certain if both of them are thought to be males or female and male nor what they did to prepare if this is a depiction of anal sex. The famous Papyrus 55001 (the "Turin Erotic Papyrus") shows many sexual positions, all of them between man and woman, but none of them seems to depict anal sex.

Literary proof for anal sex is equally rare. Famous is the tale of Horus and Seth, in which Seth tries to humiliate his opponent Horus by raping him in his sleep.

jw=w (Hr) sDr m pA s (2)

They lay down as the two men

xr-jr m grH jw stX (Hr) Di.t nxt Hnw=f

Then, in the night, Seth caused his phallus to be strong (=erect)

jw=f (Hr) Di.t Hnw=f r-jwd mnt,j<(Du.)> n Hr,w

He caused it to go speedily between the thighs of Horus.

(Papyrus Chester Beatty I, recto, 11,3-4)

This could basically support what u/otterbitch has written about the ancient Greeks. But as this is a mythological tale one can't be certain whether this is an accurate description of what homosexual intercourse would have looked like in Ancient Egypt. There's also a slightly different version of this text from the Middle Kingdom, sadly in very fragmented state, which uses xpd (buttocks, rear part) rather than mn.t (thigh), though in a slightly different context, too, as it is Isis who advises her son, Horus, on how to counteract the apparent rape by Seth. Still this could point to a description of actual anal sex, though the Papyrus doesn't include one in its current fragmented state.

jr-m-xt rDi.n=f n=k pH,tj xr=k xAa=k Dba.(Pl.)=k jm.wtj-nj xpd.w.(Pl.)=k

If he puts his strength upon you, you have to put your fingers between your buttocks.

(Papyrus Kahun VI.12, recto, X+2,6-7)

In the beginning of that Papyrus Seth praises the beauty of Horus in quite a peculiar manner.

nfr.wj pH,(wj)=kj wsx(?) rd.wj=[k]

Beautiful is your behind, broad (?) are [your] legs (?).

(Papyrus Kahun VI.12, recto, X+2,1)

There's not much else to be said about anal intercourse in Ancient Egypt, whether between male/male or female/male. We just don't know - the concept was certainly known, but we don't know the specific details you are looking for.

There are a few recipes for contraceptions, aphrodisiacs and the like, but none (as far as I know) for lubricants. There are many recipes for enemas, too, but all of them appear in regular collections for medical instructions and none of them point to a sexual use.

Edit: Added links to pictures of the mentioned items.

Follow up question, what would be used as lubricant?