Lab rats are people, too.
Does your lab rat have any outside interests or hobbies? (Real life researchers – scientists and engineers – usually do.) If so, she may occasionally need to leave the covenant to pursue them. Even one that doesn’t take her far from the covenant – like going up the road to play chess with the local abbot or fae lord – is potential story fodder. Likewise, even a lab rat might be once in a while be interested in going on vacation/pilgrimage, whether to get away from it all or see a famous magical site.
Also, circumstances often arise in life that you have to respond to no matter what you’d rather be doing. For instance, most SGs will eventually run story arcs that pose a threat to the entire covenant. Your maga might rather be in her lab, but if, say, a diabolist murders one of her covenant-mates, she’s going to have to do something about it. Likewise, all magi are members of a larger society – the Order. If one of her sodales makes enemies, she may inherit them by association. (“Sodalis Quaesitor, I really don’t think you need me to testify regarding my covenant-mate’s recent actions. Oh, you do? Very well, then.â€)
Many of the other posters have listed reasons that a lab rat, qua lab rat, would want to get out of the covenant (vis, familiars, investigating others’ original research, etc.), but an SG should be able to craft an adventure in which being a lab rat was “how you got into this mess†rather than the object of the quest. (“The colentes arcanorum have ordered you to destroy your research? That’s terrible, sodalis! What? Of course, I’d be happy to help you hide the Grimoire of Uncleane Incantationes from those small-minded fools. I get to read it, right?†or “Redcap Marco, you say there’s a violent hedge wizard in the forest who appears to violate the Limit of Energy? Hmm… Maybe I could trick him into telling me his secrets. Of course, to do that, I have to make sure the hoplites don’t get to him first…â€)
Additionally, a lab rat need not necessarily be antisocial. Especially in house Bonisagus (whose magi are far more interested in sharing their research than is usual in the Order), it’s quite possible for your Bonisagus lab rat to make friends and correspond with magi who are researching fields she finds interesting. That’s also potential story fodder. (“Salve [Bonisagus lab rat maga]! We understand that you were a friend of our late covenant member [other Bonisagus lab rat]. His recent Final Twilight has had some interesting repercussions, and we would be grateful if you could spare the time to come and investigate them. Frankly, your magic theory score was higher as an apprentice than any of ours has ever been, and we’re tired of having to put the grogs’ ears back on.â€)
Hope some of this is helpful.