The Haar system on \((0,1)\) is defined by the following equalities: \(\chi_0^0(t)=1\), \(\chi_n^k(t)=2^{n/2}\) for \(t\in ((k-1)2^{-n},(k-1/2)2^{-n})\), \(\chi_n^k(t)=-2^{n/2}\) for \(t\in ((k-1/2)2^{-n},k2^{-n})\), and \(\chi_n^k(t)=0\) for the remaining values of \(t\in (0,1)\), where \(1\leq k\leq 2^n\) and \(n=0,1,\dots\;\). Every sequence \(\lambda=(\lambda_1,\lambda_2,\dots)\) generates a multiplier \(\Lambda\) given by the equality \(\Lambda(\sum c_n \chi_n)=\sum \lambda_n c_n \chi_n\), where \(\chi_n\) are functions from the Haar system. First, the authors show that if \(\Lambda\in L(L_p,L_q)\) (the space of linear continuous operators from \(L_p\) into \(L_q\)) then \(\Lambda\in L(L_{p,r},L_{q,r})\) for every \(r\in [1,\infty]\); here the symbol \(L_{p,r}\) stands for the corresponding Lorentz space. Next, the authors study the question on conditions for \(\lambda\) ensuring the containment \(\Lambda\in L(L_{p,\infty},L_{p,1})\). Finally, the author presents some results connected with the property for the pair \(L_p,L_q\) to be exact.