Hi Harold,
Welcome to the Pond.
Lilypond does a pretty good job (actually, not just pretty good, but amazing) left to it's own devices, but music scoring is so rich that there are situations where you may need to help it out a bit. The virtue of lilypond is that there are tweaks and adjustments available from very simple to really advanced using Scheme, the lilypond extension language.
What I do in this case is manually adjust the beam, something like the following.
It's a good idea to always use bar checks at the end of a measure. Saves many headaches.
As always I really recommend using the new development versions, they are very stable and it is only the conventional open source tradition of self deprecation that labels them as 'unstable' (but even this view is controversial on the list). There's so many more features and I hammer 2.19.81 professionally all day and have not been able to crash it.
As a final point, all the beam slopes here I find personally quite ugly and ragged. There are techniques to address this, but for another email.
Andrew
====
\version "2.19.81"
lh = { \change Staff = "down" \stemUp }
rh = { \change Staff = "up" \stemDown }
\new PianoStaff <<
\new Staff = "up" {
\new Voice {
\numericTimeSignature
\lh a16
\rh e' a'
\lh a
\rh e' a'
\lh a
\rh e' a'
\lh a
\rh e' a'
\lh a
\rh e' b' e' |
\lh a
\rh e' a'
\lh a
\rh e' a'
\lh a
\rh
e' a'8.
\lh b16
\once \override Beam.positions = #'( 5 . 5.5)
c'
\rh e' g' b' |
}
}
\new Staff = "down" \with { \clef "bass" \numericTimeSignature }
{ s1 s1 }
>>
====