Both of you are correct Its the "error correction" between the Xtal you use in the PLL loop (your replacement 10.240) and the tripler.
The following deals with PLL's that use single reference Xtals - the all-in ones that many Expo kits used to synthesize - but only if you have a working "tripler / Exciter" the PLL can parse with...
Firstly the radio needs the right PLL - if you ever see a trimmer cap on the 10.240 Xtal - and heard the radio thru a known good and tuned radio on SSB mode for the same channel - you'll hear the heterodyne as they BFO while you turn the trimmer in that radio as you TX and hear it thru the other one..
Now, you can say to yourself - if this is possible - can I do more. Well, yes, but before you break out your Trident and try to harness lightning - remember there are limits - so put out the St. Elmos' Fire, Put Down that lightning rod of a Trident - and step back inside before Mother Nature decides to take you up on that offer - whether you're ready or not...
There is also the issue of generating the proper IF image - if you say use a 10.240 Crystal filter and the radio is using a 10.690 Xtal - you have to remove the 10.240 RX crystal and sub in a RESONATOR.
That's these little guys...
The above is a filter but not as "tight" as a Crystal one - and note the stamped frequency 10.75 - so it means it can be used in an IF strip of 10.7. IT also has a BANDWIDTH product - it peaks at 10.7 but it can let 10.4 ~10.3 thru - it's a lot quieter receiver but it can work...
The 455kHz - you would have an UPPER image from the PLL's switching in the 2nd cap to lower or parse down the 2nd IF to 455kHz...
There is also a PLL or two that is programmed to automatically shift 455kHz in one mode or the other - so you know...the 455kHz shift is generated inside the PLL so the above may not apply to you...
If you tried to go outside too far, the error between the free-running tripler and it's method to send the PLL a reference frequency is too great - and the PLL simply goes into out of lock condition. There is a low-pass filter with values you'd have to change to make it so...
But in a "exciter" running radio - the free running is different - you just have to use an Xtal that is close to what you already have - it just needs to make the IF part 44kHz shift. So your Xtal doesn't have to be all that much different - it's almost like you'd need a cruddy Xtal to make this work.
Now, if you were to use - say a 10.695 or 10.7 - you can get away with it - but your frequencies would be way off the channel plan. I've had several radios come thru with people thinking "instant oddballs" using a 10.695 crystal - and yes you would have oddballs but only upper range and you'd have to have someone else with a similar setup to use this method.- at least to communicate - It's possible and its' been done - I've had to undo those "Monsters" and the users are not kind to their radios' - it's a butcher job.
The Realistic one I had an S-2 for was for lowers, and it REPLACED the 10.240. And it was designed to be switchable - one Xtal (10.240 for standard 40) and the other Xtal for the lowers.
Now one thing I did mention and I'll mention again is the "divisor" frequency that is your typical 10kHz spread between channels - it's different (no you're not changing IT - the frequencies it generates will be different (doh!) but also in spacing it thinks is correct - in LOWER frequencies the bandplan offsets changes to longer counts for the 10kHz fewer counts (in the same timing frame) means longer term for divide that shift is downward up to 2kHz lower as you approach Channel 1 (the lowest frequency) Its' slower. But - in higher/uppers the bandplan "shrinks" by as much 2kHz at the ends of the band it works in (channel 40 - or the highest frequency). In uppers it's speeded up. Simply due to the timing function the PLL looks at - its' not smart - but it looks at a deviation requirement - that being the other loop to obtain your first mixer Frequency (about 16~17MHz). So if you have a typical 17MHz oscillator "exciter" for say a Cobra 19 plus, your 10.240 Xtal for Lowers is just a hair under 10 MHz (about 9.7 to 9.8MHz) while the uppers is about 10.55 - why not the 44kHz? Because of the way the PLL divides down the loop frequency - your N count - and the Exciter frequency that is pre-set and doesn't change its' "window". You are still stuck with the 16~17MHz oscillator that the exciter is. Although - the results of the shift AFFECT the "window" because of the Xtal is slower (as in lowers) - so you don't want to go out of range - just enough deviation from 10.240 to obtain the channel 40 below Channel 1 and the Channel 1 below the 40 of that.
I posted the above in reference to the Divider counter in the PLL - it uses the 10.240 timebase as the clock in which to reference the count itself in the F-Input pin from the VCO main oscillator - so as you go slower - the VCO tries to do the same - again all tied back to the 10.240 reference. It needs to know where to start and it's programmed to use that to do so.
Now in a Galaxy - that's a whole other ballgame.
(the above is a rough draft - subject to correction as I locate more of my notes...)