Meaning of this sentence in Lolita? [closed]

Here is the paragraph from Vladimir Nabokov's Lolita-

My task proved simpler than either of us had anticipated. Save for the correction of obvious solecisms and a careful suppression of a few tenacious details that despite “H.H.”‘s own efforts still subsisted in his text as signposts and tombstones (indicative of places or persons that taste would conceal and compassion spare), this remarkable memoir is presented intact. Its author’s bizarre cognomen is his own invention; and, of course, this mask—through which two hypnotic eyes seem to glow—had to remain unlifted in accordance with its wearer’s wish. While “Haze” only rhymes with the heroine’s real surname, her first name is too closely interwound with the inmost fiber of the book to allow one to alter it; nor (as the reader will perceive for himself) is there any practical necessity to do so. References to “H.H.” ’s crime may be looked up by the inquisitive in the daily papers for September-October 1952; its cause and purpose would have continued to come under my reading lamp.

Please explain the phrase in bold.

I don't understand the "would have continued to come" part.

You have mis-cited that para­graph. Your ci­ta­tion is miss­ing crit­i­cal text:

its cause and pur­pose would have con­tin­ued to [DELETED: re­main a com­plete mys­tery, had not this mem­oir been per­mit­ted to] come un­der my read­ing lamp.

In full that paragraph reads:

My task proved sim­pler than ei­ther of us had an­tic­i­pated. Save for the cor­rec­tion of ob­vi­ous sole­cisms and a care­ful sup­pres­sion of a few tena­cious de­tails that de­spite “H.H.” ’s own ef­forts still sub­sisted in his text as sign­posts and tomb­stones (in­dica­tive of places or per­sons that taste would con­ceal and com­pas­sion spare), this re­mark­able mem­oir is pre­sented in­tact. Its au­thor’s bizarre cog­nomen is his own in­ven­tion; and, of course, this mask—through which two hyp­notic eyes seem to glow—had to re­main un­lifted in ac­cor­dance with its wear­er’s wish. While “Haze” only rhymes with the hero­ine’s real sur­name, her first name is too closely in­ter­wound with the in­most fiber of the book to al­low one to al­ter it; nor (as the reader will per­ceive for him­self) is there any prac­ti­cal ne­ces­sity to do so. Ref­er­ences to “H.H.” ’s crime may be looked up by the in­quis­i­tive in the daily pa­pers for Septem­ber–Oc­to­ber 1952; its cause and pur­pose would have con­tin­ued to re­main a com­plete mys­tery, had not this mem­oir been per­mit­ted to come un­der my read­ing lamp.

I pre­sume that this makes more sense for you once the miss­ing text has been re­stored so that you have its full sentence again:

Its cause and pur­pose would have con­tin­ued to re­main a com­plete mys­tery, had not this mem­oir been per­mit­ted to come un­der my read­ing lamp.