How can I get three diacritics on the same Greek letter?
You can use the character combination already provided in the font:
\documentclass{article}
\usepackage[greek.polytoniko,english]{babel}
%\usepackage{fonttable}
\DeclareRobustCommand{\combinedaccent}[2]{%
\leavevmode\vbox{\offinterlineskip
\ialign{\hfil##\hfil\cr
\char#1\relax\cr
\noalign{\vskip -1ex}
\noalign{\vskip 0.1ex}
#2\cr
}%
}%
}
\newcommand{\lb}[1]{\combinedaccent{96}{\={#1}}} % barys
\newcommand{\lo}[1]{\combinedaccent{39}{\={#1}}} % oxys
\newcommand{\lob}[1]{\combinedaccent{126}{\={#1}}} % oxybareia
\newcommand{\ld}[1]{\combinedaccent{60}{\={#1}}} % dasia
\newcommand{\ldb}[1]{\combinedaccent{67}{\={#1}}} % dasia barys
\newcommand{\ldo}[1]{\combinedaccent{86}{\={#1}}} % dasia oxys
\newcommand{\ldob}[1]{\combinedaccent{64}{\={#1}}} % dasia oxybareia
\newcommand{\lp}[1]{\combinedaccent{62}{\={#1}}} % psilon
\newcommand{\lpb}[1]{\combinedaccent{95}{\={#1}}} % psilon barys
\newcommand{\lpo}[1]{\combinedaccent{94}{\={#1}}} % psilon oxys
\newcommand{\lpop}[1]{\combinedaccent{92}{\={#1}}} % psilon oxybareia
\begin{document}
\textgreek{\lb{a}\lo{a}\lob{a}\ld{a}\ldb{a}\ldo{a}\ldob{a}\lp{a}\lpb{a}\lpo{a}\lpop{a}}
\end{document}
The teubner
package defines a more comprehensive set of macros for combined accents, compared with @egreg's answer. Here's Table 4 from the documentation (teubner-doc.pdf):