Thank you all!
- Diane - now I understand, thanks - a useful approach as I research further.
- Jeremy - thanks for the JC tip, I've taken a look and see more can be done here.
- Off-list, Eva - thanks so much for doing those searches. Intriguing possibilities, but as you'll see below, I think they're probably unconnected.
- Off-list, Sherri - thanks, I did consider the 'cad using a false name' as a last resort, intriguing too but very hard to research.
- Off-list, Amit - thanks, even though my problem was Isidor not Eva.
- Others I may have forgotten en route - thank you too!
- Sheryl - wonderful! I'm sure at least some of those are him, and those SA websites in general are a great way to look for more info. Specifically, they mention that ship...
I've now managed to piece together more of the puzzle, thanks to a hitherto unidentified letter combined with the information above. It seems Isidor and Eva went to Cape Town (the ship Kenilworth Castle, departing 16 Dec 1905 has a "Mr J Lasker"), then Port Elizabeth (staying at "the Royal", presumably a hotel), where "his business collapsed". The marriage didn't go well - by September 1906 she was complaining that "Jimmie" was treating her like a dog - gambling, drinking, threatening to kill her, frustrating her attempts to get "a situation" (a job?) by telling people they weren't married, and so on. So she fled to "a decent berth" (job?), "15 pounds a month with board and lodging" at the Queen's Hotel, Umtali (Rhodesia) - they even paid her "expensive" fare for the week-long train journey there. And although she did leave "Jimmie" a letter offering to return if he treated her better, she didn't tell him where she was going, out of fear he would make himself such a nuisance that she would have to give up her "situation" (again, does this mean some sort of hotel work? secretary? dancer? who knows...). She also says she has used her maiden name when "taking a situation" as "it is the normal thing here".
What happened next, I don't yet know. The letter was written to her father (a well-known academic) the same day he died in mysterious circumstances... (Anyone fancy making a book/film of this?!) So it may take more research, probably delving deeper into South African and Rhodesian data (both official records and newspaper reports etc.), if there are any.
The 1890 Isadore/Jennie marriage is possible... maybe they split before his UK (re)marriage in 1905, or Jennie died. But if they were "pre 1890 settlers", where did he come from before then - where is his father Aaron Lasker? And why would he be applying for naturalization in 1906? Maybe the 1906 "APPLICATION FOR LETTERS OF NATURALIZATION. ISIDOR LASKER." were an application on behalf of his new wife Eva?
The 1928 death is rather confusing - age 67 implies he was born 1861 (whereas the UK marriage certificate implies born 1867; a six year difference is not impossible, but still...). I note there's also a Jane Lasker dying at the same location in 1926 age 56, so an implied wife. Did Eva just say "I'm widowed" at her remarriage in 1918 because she assumed/pretended he was dead, whereas in fact he'd survived, remarried Jane (third wife?) and lived on? I'd need to find a marriage record for Isidor/Isadore + Jane.
So, overall I think I now have a good initial grasp of what happened, thanks to everyone here, although numerous questions remain. A simple one for now: "Isidor/Isadore" appears to be a Greek name, 'gift of Isis'. I'm guessing she called him "Jimmie" just as a random 'pet name', not because it's a common abbreviation for Isidor, right? And although I've come here because I blithely assumed he was Jewish, I've not actually seen any evidence for that fact - is it a reasonable assumption?