Statement-1 : Hydrogen atom consists of only one electron but its emission spectrum has many lines.

Statement-2 : Only Lyman series is found in the absorption spectrum of hydrogen atom whereas in the emission spectrum, all the series are found.

Every atom has certain definite energy level. In the normal state, the electron in the hydrogen atom stays in lowest energy level. When the atom gets appropriate energy from outside, then this electron rises to some higher energy level i.e. atom is excited. Within nearly ${10}^{-8} s$, the electron leaves the higher energy level. 

Now, it can return either directly to the lowest energy level (or the ground state) or come to the ground state after passing through other lower energy levels. Since there are a large number of atoms in a light source (hydrogen lamp), all possible transitions take place in the source and many lines are seen in the spectrum. The slit gives the shape of the spectrum and large number of lines are obtained because a large number of atoms are getting excited and de-excited to different energy levels. 

At ordinary temperature, all atoms are present at their lowest energy level (n=1). Hence absorption transition can starts only from n=1 (and not from n=2,3,4,..). Hence only Lyman series is found in the absorption spectrum of hydrogen atom whereas in the emission spectrum, all the series are found.