The real answer is: "As big as your novel or game needs it to be."

A "lord" is not really a specific rank, it just means a noble who is in charge of some land/people.

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A lord could hold a single castle on the border with a small retinue of a few dozen men. A lord could be a powerful Duke whose forces are greater than even that of the king.

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What should be remembered is this:

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- A lord's 'permanent' army was usually rather small. These would be soldiers that are garrisoning castles, keeping the peace, patrolling dangerous areas, serving as bodyguards and honor guards, hunting bandits, and that sort of thing.

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- If a campaign was in the works, the army would grow in size with plenty of part-timers, both professional and not. Medieval Europe was awash in bands of armed men who would join up on campaigns for payment and a share of the loot. A campaign was generally rather short and would involve a lot of temporary soldiers/mercenaries.

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- Any medieval army was limited by its supply. Supply lines as we think of them today didn't really exist back then. The army would requisition (this usually means "steal") food from whichever area they happened to be in at the time. You can see how thousands of armed and violent men are not exactly a welcome sight even in 'friendly' lands, so a large standing army simply could not exist without completely denuding the countryside of food. This was of course why you'd want them to be doing this in enemy territory. Fantasy novels/games tend to anachronistically avoid or ignore this because they tend to have some sort of Good Guy Army and it would look bad if they are robbing and raping the populace. For all its faults, Game of Thrones (the books at least) seem to understand that large mobs of armed soldiers are dangerous to everybody, regardless of allegiance.

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- Soldiers aren't in your army for patriotic reasons, for the most part. Your army is likely made up of men from different places with the main unifying factor being their quest for glory and profit. Your recruitment target is not "nationalistic idealists" - its "professional armed killers with free time and greed".

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-Armament: There was no centralized supply depot. Soldiers would arm themselves. Depending on their social rank this could be with heavy mail, horse, lance, and sword or something far simpler like a bow + knife, or spear + helmet. Wealth played a big role. There was no standardization. Everything was handmade by different people in small numbers so you would not see much uniformity.

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- Any medieval army has followers. Farriers, smiths, prostitutes, merchants, fletchers, priests, and people of every sort would be tagging along with an army. These would typically stay out of the dangerous areas and stick with the baggage train. Raiding an enemy's baggage train could be devastating to them.

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- Field battles were rare. Sieges were far more common, but would usually not involve epic movie-style trebuchets and masses of men getting shot by arrows as they stormed the walls. Usually it would be a boring affair, with the invaders attempting to starve out the defenders, with missile fire being exchanged and some small raids and sallies from the castle. The most likely end of it would be :

- Relief coming to the defenders, and the attackers must engage the relief force or retreat.

- The attackers giving up and going home if their food runs out before the defenders.

- The defenders surrendering when the situation gets serious. Sometimes this would involve treachery from within.

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It was very unlikely for the attackers to storm the castle unless they had some major advantage. If they did storm the castle then the defenders could expect quite a lot of looting, rape, and violence. If they surrendered willingly, then they would be treated more fairly.

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- Most medieval campaigns featured lots of looting, pillaging, raiding, and skirmishes rather than gigantic open field battles where thousands of men died at once. You were more likely to die in a minor engagement or from the plethora of diseases available than in an epic pitched melee.

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