There is no problem with having a lid on your kettle during portions of the boil. However the duration that the lid needs to be off the kettle does vary in accordance with the grist composition. While a maximum of about 30 minutes is all that is required to remove any existing DMS in your wort, the remainder of the boil period can be fully covered with no ill effect.
Covering the kettle is actually a useful measure for reducing heat stress on your wort. With the lid on, the heat input can be reduced. Any SMM in the wort is still converted to DMS at the same rate as a full open boil as long as your wort is still at boil temperature. As soon as you open the lid and resume a good rolling boil, the DMS will be expelled in about another 30 minutes.
While I understand your concern with stuff falling into the kettle, its better to reduce the evaporation for a portion of the boil duration. So placing a screen over the kettle isn't ideal for either the covered or uncovered stages of boiling since it allows atmospheric exchange of both too little and too much. You really want All or Nothing, not Sort Of or Semi.