  The boundary of the lemon billiards is defined by the intersection of two
circles of equal unit radius with the distance $2B$ between their centers, as
introduced by Heller and Tomsovic in Phys. Today {\bf 46} 38 (1993). This paper
is a continuation of our recent paper on classical and quantum ergodic lemon
billiard ($B=0.5$) with strong stickiness effects published in Phys. Rev. E
{\bf 103} 012204 (2021). Here we study the classical and quantum lemon
billiards, for the cases $B=0.42,\;0.55,\; 0.6$, which are mixed-type billiards
without stickiness regions and thus serve as ideal examples of systems with
simple divided phase space. The classical phase portraits show the structure of
one large chaotic sea with uniform chaoticity (no stickiness regions)
surrounding a large regular island with almost no further substructure, being
entirely covered by invariant tori. The boundary between the chaotic sea and
the regular island is smooth, except for a few points. The classical transport
time is estimated to be very short (just a few collisions), therefore the
localization of the chaotic eigenstates is rather weak. The quantum states are
characterized by the following {\em universal} properties of mixed-type systems
without stickiness in the chaotic regions:(i) Using the Poincar\'e-Husimi (PH)
functions the eigenstates are separated to the regular ones and chaotic ones.
The regular eigenenergies obey the Poissonian statistics, while the chaotic
ones exhibit the Brody distribution with various values of the level repulsion
exponent $\beta$, its value depending on the strength of the localization of
the chaotic eigenstates. Consequently, the total spectrum is well described by
the Berry-Robnik-Brody (BRB) distribution.
