He received his initial musical education at the Baghdad Conservatoire (or the Model School of Music & Ballet, 1970–71; 1972–81), where he was classically trained by Soviet, Hungarian, and Arab music teachers, and spent some of his formative years in Kuwait City (1967–70), and Cambridge, England (1971–72), where he began to learn English at the Church of England Grantchester Primary School. He pursued his musical studies in Vienna and Salzburg (1981–85), Kent, Ohio (1985–88), Austin, Texas (1988–93), as well as San Francisco, and Los Angeles, California (1994–96 and 1998-2000, respectively).
Having studied conducting with Peter Richter de Rangenier at the Vienna Music University, with Frank Wiley at Kent State University, Kent, Ohio, and with Louis Lane at The University of Texas at Austin, Lulua received further practical training from the San Francisco Symphony and the Los Angeles Philharmonic Orchestra, Herbert Blomstedt and Esa-Pekka Salonen, music directors, respectively.
Lulua has conducted performances in the Middle East, Europe and the United States since 1978, and founded several orchestras, such as The 'Ur Orchestra in Austin, Texas and Philharmonia Scotland in Glasgow.
Lulua was invited by London-based American composer Stephen Montague to contribute to the BBC Symphony Orchestra-sponsored "John Cage UnCaged Musicircus" at the Barbican Centre, London in 2004.
In a 2009 masterclass guided by Maestro Jorma Panula with the Rousse Philharmonic Orchestra in Bulgaria, Bashar conducted the first movement of the Resurrection Symphony by Gustav Mahler. He returned to Bulgaria in 2013 to conduct Act 3 of La bohème at the Burgas State Opera.
Lulua is the Principal Guest Conductor of the Camerata Miskolc in Miskolc, Hungary, and has recorded rarely performed works with them, such as Antonín Dvořák's Notturno in B, op. 40, Carl Nielsen's Little Suite for strings, op. 1, and Jean Sibelius' Romance in C, op. 42, Impromptu, and Rakastava (The Lover), op. 14.
He is a naturalised citizen of the United Kingdom.