If King brokers a peace deal at Ibrox and is put forward for a position on the board, Lawwell admits that he will need to consider his role in the process.
Having reached a settlement with the South African Revenue Services by paying £45m in tax arrears and fines totalling around £700,000 after he was convicted of 41 breaches of the Income Tax Act, King believes there is no impediment to him joining the Rangers International Football Club board, not least because he continues to be executive chairman of Micromega, his investment firm that is listed on the Johannesburg Stock Exchange. Any appointment would need to be ratified by the nominated advisor managing RIFC's listing on the Alternative Investment Market, and also by the SFA.
The governing body would take into account the period King spent on the board after Craig Whyte took over as owner, preceding Rangers going into administration then liquidation last year. King will have to present submissions on both issues to the SFA's professional game board, which includes Lawwell, although the former Rangers director is confident of his case.
Lawwell described it as a "complex issue" that may have to be considered by the main SFA board instead, but he will judge what role he should play as the chief executive of Rangers' city rivals. When Celtic Park was being considered as one of several potential venues for this season's Scottish Cup final, Lawwell excused himself from the decision-making process, which eventually awarded the final to the stadium, although supporters of other clubs have voiced their dissent.
"My main interest is to promote and maximise the interests of Celtic," Lawwell said. "But I wouldn't have taken the job on the SFA board if I felt the two couldn't be aligned. There are areas where there will be conflict, no question, like the Scottish Cup final, where there were other bidders. I will do the job properly. There will be sensitive issues, but I don't think there will be too many where I would be conflicted.
"There's maybe one or two coming up. On any board, if you feel you are conflicted, you would excuse yourself. It depends, which club, who it is. Are we conflicted more than Hibs? It's SFA business, I haven't even thought about it, I haven't even discussed it."
Lawwell is hopeful of concluding contract negotiations with Georgios Samaras and Joe Ledley before the January transfer window. "We're meeting Sami's guys in the next week and we're in constant discussion with Joe's, so hopefully we get some form of resolution before the end of December," Lawwell said. "Both are keen to stay and both realise what it means to play for Celtic."