The big disadvantage to LyX is that it's not LaTeX editor but a LaTeX generator. So if you want to write your next article or dissertation and can commit to it then it's great, but if you want to import work so far or collaborate with someone not using LyX then it doesn't really work (it has an import function but it's almost unusable).
Once you've done that once in the session, you can just hit C-\ to toggle it on and off (C-x RET C-\ [input method] actually lets you select from a wide variety of input methods, and C-\ toggles on and off the most recently selected input method).
Greek letters are always a latin letter followed by an asterisk. Arrows and comparison operators are what one would guess. Mathematical symbols generally make some sense:
<C-k> a * α
<C-k> F * Φ
<C-k> = > ⇒
<C-k> - > →
<C-k> > = ≥
<C-k> 0 0 ∞
<C-k> d P ∂
<C-k> I n ∫
I have a standard keyboard and I type greek letters easily. ALTGR+a, and so on.
If somebody is not able to configure their keyboard to do this they are not probably writing LaTeX, either.
(Admittedly, this anecdata is even more useless than usual.)
As long as you don't need caps lock as your escape key...
It follows a set of rules so you don't have to remember a large number of sequences but can often guess the right one intuitively.
ASCII digraphs for mathematical operators give the corresponding operator, e.g., <= yields ≤.
Greek letters are given by an asterisk followed by a corresponding latin letter, e.g., *d yields δ.
https://9fans.github.io/plan9port/man/man7/keyboard.html
There's a program (mklatinkbd) to convert it to a format usable with X11.
Well, LaTeX itself is not very discoverable either
Ctrl-k a Shift-8