© Alberto Policriti and Nicola Prezza. The Lempel-Ziv factorization (LZ77) and the Run-Length encoded Burrows-Wheeler Transform (RLBWT) are two important tools in text compression and indexing, being their sizes z and r closely related to the amount of text self-repetitiveness. In this paper we consider the problem of converting the two representations into each other within a working space proportional to the input and the output. Let n be the text length. We show that RLBWT can be converted to LZ77 in O(n log r) time and O® words of working space. Conversely, we provide an algorithm to convert LZ77 to RLBWT in O(n(log r + log z)) time and O(r + z) words of working space. Note that r and z can be constant if the text is highly repetitive, and our algorithms can operate with (up to) exponentially less space than naive solutions based on full decompression.