Excellent questions! The direct quote from Lincoln to Scott was " If it shall be to arm their people against the United States, he is to
adopt the most prompt, and efficient means to counteract, even, if necessary, to the bombardment of their cities." Many follow on historian (I did not name names or book titles) claim that what Lincoln meant was if Maryland seceded and was to join in arm insurrection against the Union - then Scott was directed to bombard Maryland's cites. However, these instructions were immediately passed from Gen. Scott to Gen Butler who would be a primary commander in the attack against Baltimore. It certainly appears that these instructions were to be implemented if the militias in Baltimore resisted the attack by the four regiments to attack the city. That the indiscriminate bombardment of the city was authorized by the President if they resisted. Further evidence was that after the "Battle of Baltimore" was over Gen. Butler proclaimed that if anyone shot at the troops passing through Baltimore then he would "blow up their house." We also have the guns on Federal Hill and of Ft. Mchenry trained towards the city itself.
I think Lincoln's instructions to "bombard their cites" had an impact on the Governor and the State Legislature since the Legislature proclaimed in early May that they would not arm their militia or take any action that could be construed as "hostile" towards the federal government. Shortly after and starting in May Gov. Hicks ordered the collections of all State arms held by the state militia and had them turned over to the Federal forces. The Maryland Legislature investigated this and proclaimed that Governor's actions violated the Maryland Constitution, but they also stated that they would not re-arm the Maryland militia. This dis-arming of Maryland is a major point in the analysis of the arrest of the Legislature in September. Gen. Dix knew full well Maryland was disarmed, almost fully occupied and I quote Dix as stating that there was "no difficulty in holding Maryland militarily." By the time the Legislature was imprisoned, Maryland had no military force to resist, had been occupied by an overwhelming force of Union troops and any Marylander who wanted to take arms against the Union had already left the State.
As to your second rounds of questions, yes I do detail much but not all of what you said. An entire book could be written on what transpired in April / May 1861. At this point in time Hicks publicly proclaimed he wanted Maryland to remain neutral, but he soon turned towards and supported Lincoln's policies both nationally and towards Maryland. As stated above Hicks was instrumental in de-arming the Maryland militia and I have numerous citations of his communications with the Union Generals and vis versa. After leaving office Hicks was re-warded by Lincoln with a commission as a Union General. Early after the civil unrest on the 19th both Baltimore Mayor Brown and Gov. Hicks did not want more troops to pass through Baltimore. This was not because they wanted to openly defy the President but because the reality was that the citizens of Baltimore were hugely agitated and they knew that any further passing of federal troops would lead to violence on a scale far larger than what was seen on the 19th. I re-iterate that this was because of the agitation of the people and the government of Maryland took measure to avoid conflict. Since you are very sophisticated in CW history, I probably don't have to tell you that their agitation was based upon the North using force against the states and had nothing to do with abolition. Both Pres. Lincoln and Gen. Scott agreed that they would march around Baltimore and use other routes. Mayor Brown agreed that he would work to get his people under control and will protect the federal troop to the best of his abilities.
As to Lord Lyon's acting as a mediator, I believe that proposal related to Lyons being a mediator between Lincoln and Davis, but that idea seemed to have fissiled. I do briefly talk about how the Maryland Legislature sent "peace commissioners" to meet with Lincoln and Davis asking them to hold off on any hostilities until Congress convened and hopefully broker a resolution acceptable to all. That also did not go anywhere though the Maryland peace commissioners were sent.
Gov. Hicks did communicate to Pres. Lincoln that he could not supply the 4 regiments from Maryland at that time due to the agitated state of affairs in Maryland. I believe this was within the April 22 communication you refer to. However, it was not long afterwards that Hicks informed Lincoln that he would supply the President the regiments of Marylanders and there was an agreement that the Marylanders would only be used for the protection of the Capitol itself or within Maryland. Though such was agreed to, the limitation on using Marylanders only in Maryland or for the defense of the Capitol was not honored by the President.