Even minor modifications, such as making double heat sinks available, tend to make a huge difference in play style while in-universe costing relatively little as a percentage of the cost of the hardware in a battlemech. Page TM221 tells us that DHS were recovered (that is, are back to full scale industrial production) by 3040 by the Federated Suns (thus 12 years or 3 Tour of Duty life cycles) , but the information required for the development should be available to everybody 3029ish due to the availability of the Helm Memory Core.
A good way to add lostech equipment is having your company come into contact with one of those merchant jumpships that are spreading around copies of the Core. How tech-savvy is your support personnel?
Another alternative is having them find a good old SLDF cache, with a few lostech units and a certain amount of spare parts. This tends to work better with mercenary commands, as regular House units will tend to be ordered pass these upstairs, but they could easily start doing tactical analysis of the various pieces of lostech equipment to inform their bosses of which of these is more useful and thus should be researched first. Since you are playing a game, deviations from canon should be expected.
Finally, you could always give your PCs and NPCs the equivalent experience of three or four Tour of Duty life stages, representing a timeskip with relatively generic service. Remember, though, that that represents a fair chunk of their expected career duration, and even if they don't get tangled much in the traditional Marik civil wars, odds are that the lancemates will either have been killed in action or promoted to lance or even company leader. You'd end up having to generate new characters to represent the generic shuffle of units