If it is accepted that Stefan Amaris could raise dozens of divisions in a few years from reservists (and in fairness, that's not wholly implausible given how rapidly large forces have been raised in our own history*, even given a longer and more technical training period) then it is consistent that the House Lords could raise scores of regiments in a similar time period.
I'm not challenging Amaris's ability to expand his own army; there he can build off existing table of organization and incorporate reserves. What he did is quite similar to how European armies were organized in the run-up to WWI. The rapid expansion would hurt his overall effectiveness as officers would necessarily be promoted beyond their abilities simply because there were so many new units to fill up.
* In WWII the US Army went from, IIRC correctly, ~12 regular divisions and ~12 National Guard divisions in 1945 to 91 divisions in 1945. Training mechwarriors and other 'modern' soldiers so quickly would not be possible, but it's believeable that given three or four times as long - that is, 12-16 years - that a highly industrialised society could do likewise in Battletech. Now whether they could do so secretly is another can of worms entirely.
Again, while LoT notes that training time for individuals in the SLDF is 3-8 years from joining to hitting their first unit, I'm not concerned with the expansion of the House armies; the personnel can be found; equipment is harder, but it seems 2750-2765 was a period of massive military production, since everyone but the SLDF was massively increasing their armies. Not only Amaris's 70 "secret army" divisions, but the Houses added 250 'Mech regiments between them in that time, the equivalent of another ~40-80 divisions. That big a production upswing throughout the Inner Sphere would be noticable even to military personnel who don't know much about economics. While the House military expansions would have provided some nice cover to Amaris's expansion, it would also have drastically driven up the difficulty of borrowing money for him.
The Secret Army divisions, however, have no existing force to build from. The commander of each "Secret Army" division was likely a civilian in 2758, but he/she was able to destroy more than two SLDF divisions on average in 2766. Everyone is a civilian in uniform, which means they're amateurs, which means they
should be making a lot of stupid mistakes. But the way they're described in the book makes it seem like they were extremely competent, skilled, and a challenge to the SLDF.
In WWII, the US Army increased in size dramatically, but the quality of its officer corps went down just as drastically. Anything more than a cursory study of the conflict will show that across all branches of the US military a lot of stupid decisions were made by commanders, and the US Army was essentially a bunch of civilians in uniform until late '44 early '45. Even the long-service professionals had trouble with the massive expansion, because they had never been trained to operate such large formations. But at least they were long-service military professionals -- the same can not be said for the Periphery "Secret Army" divisions or their personnel.
As to warship numbers, Amaris' method of building ships sounds plausible enough. The SLDF yards seem to have been able to churn out battleships once or twice a year without great difficulty so the prospect of a member state being able to build themselves a dozen or so large warships in a decade and a half sounds plausible, and building many smaller ships - corvettes and destroyers - in yards that usually build jumpships would also be possible (it would also fit the general proportions seen in RUW naval organisation). I doubt there would be many yards capable of building warships that the SLDF wouldn't keep control of so the slow buildup is also plausible although I admit I'd like to see the sort of fleets detailed in the Fan Book TRO 2800
The method is okay; him having the industrial base to pull it off and not get caught? Well, given how magically industry appears in the rest of the franchise, I guess I can let it slide. But his WarShip crews should have been even more incompetent than everyone else fighting, yet they manage to simultaneously seize every JumpPoint in the Hegemony despite lacking the numbers to actually do so. And all their obsolete SLN WarShips should be just as much eggshells-armed-with-sledgehammers as the regular SLN ships, but running Green crews instead of Veteran. I'm amazed that even half of them survived the initial seizure of the TH; it must have been the half who never so much as saw an SLN ship.
Irose:
Less than a hundred Makos; 5 were bought by the RWR, and the SLN had some for use as courier vessels. And others were produced post-2750, no doubt. But it does imply that the Steiner fleet was made up of nothing but Makos & Tharkads. I suppose that the House militaries could have put ships into mothballs just the same as the SLN (Amaris had 30 Pintos left over from the previous century), but even so there's not enough room for the known ships in the Lyran fleet, much less the unknown ones.